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R
Class 11 Physics - Rotation
Rotational Dynamics and Rolling Motion
Master rotational kinetic energy, work and power in rotation, rolling without slipping, combined energy, applications, numericals and PYQs.
CBSENEETJEE MainJEE AdvancedIBIGCSEA-Level
01
Rotational Kinetic Energy
Rotational kinetic energy is energy due to rotation. It depends on moment of inertia and angular speed.
Krot = 1/2 Iω2Ktrans = 1/2 mv2
Same mass can have different rotational energy if mass distribution changes I.
02
Work Done in Rotation
Rotational work is torque times angular displacement. For variable torque, integrate over angle.
dW = τ dθW = τθW = ∫τ dθ
Area under τ-θ graph gives work done.
03
Power in Rotation
Power is the rate of rotational work. Motors, fans, wheel drives and engine shafts use rotational power.
P = dW/dtP = τω
High torque at high angular speed means high power.
04
Rotational Dynamics Basic Relation
Torque is the rotational analogue of force; moment of inertia is the rotational analogue of mass.
| Linear Motion | Rotational Motion |
|---|---|
| Force F | Torque τ |
| Mass m | Moment of inertia I |
| Acceleration a | Angular acceleration α |
| Work Fs | Work τθ |
| Power Fv | Power τω |
| Kinetic energy 1/2mv² | 1/2Iω² |
| Momentum mv | Angular momentum Iω |
05
Rolling Motion
Rolling is translation of centre of mass plus rotation about centre of mass. In pure rolling, the contact point is instantaneously at rest.
- Top point velocity = 2v.
- Centre velocity = v.
- Bottom point velocity = 0 in pure rolling.
- Instantaneous axis is through contact point.
06
Rolling Without Slipping
Very important: pure rolling means no relative slipping at contact. Static friction can provide torque.
v = Rωa = Rα
Slipping and pure rolling are different; do not use v=Rω during slipping.
07
Translational + Rotational Energy
Rolling body has two kinetic energies: translation of COM and rotation about COM.
| Body | I | Krolling |
|---|---|---|
| Ring | MR² | mv² |
| Disc / Solid cylinder | MR²/2 | 3/4 mv² |
| Solid sphere | 2MR²/5 | 7/10 mv² |
| Hollow sphere | 2MR²/3 | 5/6 mv² |
08
Rolling Down Inclined Plane
Mass distribution controls acceleration and final speed.
| Body | Acceleration | Velocity | Exam Tip |
|---|---|---|---|
| Ring | g sinθ/2 | √(gh) | Slowest |
| Disc / cylinder | 2g sinθ/3 | √(4gh/3) | Middle |
| Solid sphere | 5g sinθ/7 | √(10gh/7) | Fastest |
09
Friction in Rolling
Static friction appears in pure rolling; kinetic friction appears in slipping. Static friction may do zero work on a fixed rough surface.
Pure Rolling
Contact point has zero relative velocity; friction is static.
Slipping
Contact point slides; friction is kinetic and dissipates energy.
Direction
Direction depends on tendency of slipping, not always backward.
10
Applications
Concept cards with formula, diagram and exam tip.
Rolling wheel
Concept: Translation plus rotation
Formula: v=Rω
Exam Tip: Bottom point has zero velocity.
Rolling cylinder down incline
Concept: Energy and torque
Formula: a=g sinθ/(1+I/MR²)
Exam Tip: I/MR² decides acceleration.
Rolling sphere
Concept: Small inertia factor
Formula: a=5g sinθ/7
Exam Tip: Solid sphere is fast.
Bowling ball
Concept: Rolling plus possible slipping
Formula: K=Ktrans+Krot
Exam Tip: Check if pure rolling.
Bicycle wheel
Concept: Pure rolling link
Formula: v=Rω
Exam Tip: Top point speed is 2v.
Car tyre
Concept: Static friction and rolling
Formula: a=Rα
Exam Tip: Tyre-road friction is usually static.
Flywheel
Concept: Rotational energy storage
Formula: K=1/2Iω²
Exam Tip: Large I stores energy.
Fan motor
Concept: Rotational power
Formula: P=τω
Exam Tip: Motor torque sets angular acceleration.
Yo-yo motion
Concept: Potential to translation and rotation
Formula: mgh=1/2mv²+1/2Iω²
Exam Tip: String constraint matters.
Spool problems
Concept: Torque about contact point
Formula: depends on pull geometry
Exam Tip: Direction can surprise you.
Pulley and rotating disc
Concept: String acceleration and rotation
Formula: a=Rα
Exam Tip: Pulley inertia reduces acceleration.
Rolling race
Concept: Compare I/MR²
Formula: a=g sinθ/(1+β)
Exam Tip: Small β wins.
11
Important Graphs
Graph interpretation for rotational work, angular speed, energy and rolling point velocities.
Torque vs Angular Displacement
Area gives work.
Angular Velocity vs Time
Slope gives angular acceleration.
Krot vs omega
Parabolic relation.
Rolling KE Comparison
Depends on I/MR².
Wheel Point Velocities
Top 2v, centre v, bottom 0.
12
Important Formula Table
Complete quick formula sheet.
| Concept | Formula | Meaning | Exam Tip |
|---|---|---|---|
| Krot | 1/2Iω² | Rotational KE | Use I about rotation axis |
| Work | τθ, ∫τdθ | Rotational work | Area under τ-θ |
| Power | τω | Rate of work | Motor/fan problems |
| Dynamics | τ=Iα | Rotational F=ma | Net torque |
| Pure rolling | v=Rω, a=Rα | No slipping | Use only if pure rolling |
| Krolling | 1/2Mv²+1/2Iω² | Total KE | Never forget rotation |
| Incline acceleration | g sinθ/(1+I/MR²) | Rolling acceleration | Small factor wins |
| Height speed | √[2gh/(1+I/MR²)] | Final speed | Energy method |
Searching for a Physics Tutor? If Rotational Dynamics, Rolling Motion or NEET/JEE rotational numericals are not clear, contact Kumar Sir.
Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com
13
High-Quality Numericals
Solved bank covering energy, power, torque, rolling, incline, pulleys, spools and yo-yos.
1. CBSE rotational KE: I=2 kg m² and ω=6 rad/s. Find Krot.
Question: I=2 kg m² and ω=6 rad/s. Find Krot.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: K=1/2Iω²=36 J.
Final Answer: K=1/2Iω²=36 J.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: K=1/2Iω²=36 J.
Final Answer: K=1/2Iω²=36 J.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
2. NEET work by torque: Torque 8 N m rotates through 5 rad. Work?
Question: Torque 8 N m rotates through 5 rad. Work?
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: W=τθ=40 J.
Final Answer: W=τθ=40 J.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: W=τθ=40 J.
Final Answer: W=τθ=40 J.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
3. JEE Main power: Torque 12 N m at 20 rad/s. Power?
Question: Torque 12 N m at 20 rad/s. Power?
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: P=240 W.
Final Answer: P=240 W.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: P=240 W.
Final Answer: P=240 W.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
4. JEE Advanced rolling energy: Solid cylinder speed v. Find total KE.
Question: Solid cylinder speed v. Find total KE.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: K=3/4Mv².
Final Answer: K=3/4Mv².
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: K=3/4Mv².
Final Answer: K=3/4Mv².
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
5. IB incline ring: Ring rolls down incline angle θ. Find acceleration.
Question: Ring rolls down incline angle θ. Find acceleration.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: a=g sinθ/2.
Final Answer: a=g sinθ/2.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: a=g sinθ/2.
Final Answer: a=g sinθ/2.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
6. IGCSE pure rolling: R=0.5 m and ω=10 rad/s. Centre speed?
Question: R=0.5 m and ω=10 rad/s. Centre speed?
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: v=Rω=5 m/s.
Final Answer: v=Rω=5 m/s.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: v=Rω=5 m/s.
Final Answer: v=Rω=5 m/s.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
7. A-Level solid sphere: Solid sphere descends height h. Find v.
Question: Solid sphere descends height h. Find v.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: v=sqrt(10gh/7).
Final Answer: v=sqrt(10gh/7).
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: v=sqrt(10gh/7).
Final Answer: v=sqrt(10gh/7).
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
8. Pulley inertia: Pulley radius R and angular acceleration α. String acceleration?
Question: Pulley radius R and angular acceleration α. String acceleration?
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: a=Rα.
Final Answer: a=Rα.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: a=Rα.
Final Answer: a=Rα.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
9. Yo-yo: A yo-yo descending uses energy into which forms?
Question: A yo-yo descending uses energy into which forms?
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: Translational and rotational kinetic energy.
Final Answer: Translational and rotational kinetic energy.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: Translational and rotational kinetic energy.
Final Answer: Translational and rotational kinetic energy.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
10. Friction: Pure rolling on fixed rough floor: work by static friction?
Question: Pure rolling on fixed rough floor: work by static friction?
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: Zero at contact for ideal pure rolling.
Final Answer: Zero at contact for ideal pure rolling.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
Diagram: shown above.
Given: Identify I, M, R, omega, torque, angle, height or incline.
Formula: Krot=1/2Iω2, W=τθ, P=τω, τ=Iα, v=Rω, K=1/2Mv2+1/2Iω2.
Calculation: Zero at contact for ideal pure rolling.
Final Answer: Zero at contact for ideal pure rolling.
Exam Tip: Use v=Rω only for pure rolling.
Common Mistake: Forgetting rotational kinetic energy.
14
NEET Question Bank
50 NEET-style MCQs. Authentic years are not invented.
1. NEET Exam-style Question: Rotational kinetic energy is: A 1/2mv² B 1/2Iω² C Iω D τθ
Correct Answer: B. Krot=1/2Iω².
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
2. NEET Exam-style Question: Work done by constant torque τ through angle θ is: A τθ B τ/θ C θ/τ D Iω
Correct Answer: A.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
3. NEET Exam-style Question: Power in rotation equals: A Fv B τω C I/ω D τ/ω
Correct Answer: B.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
4. NEET Exam-style Question: Rotational analogue of F=ma is: A τ=Iα B L=Iω C v=Rω D W=τθ
Correct Answer: A.
Detailed Explanation: This tests dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
5. NEET Exam-style Question: Pure rolling condition is: A v=Rω B v=ω/R C a=ωR² D I=MR
Correct Answer: A.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
6. NEET Exam-style Question: Total KE of rolling body is: A translational only B rotational only C 1/2mv²+1/2Iω² D zero
Correct Answer: C.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
7. NEET Exam-style Question: Rolling KE of ring is: A 1/2mv² B mv² C 3/4mv² D 7/10mv²
Correct Answer: B.
Detailed Explanation: This tests ring rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests ring rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
8. NEET Exam-style Question: Rolling KE of solid disc/cylinder is: A mv² B 3/4mv² C 5/6mv² D 7/10mv²
Correct Answer: B.
Detailed Explanation: This tests disc rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests disc rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
9. NEET Exam-style Question: Which rolls fastest down same incline: ring, disc, solid sphere?
Correct Answer: Solid sphere, because I/MR² is smallest.
Detailed Explanation: This tests incline race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
10. NEET Exam-style Question: In pure rolling on fixed rough surface, static friction at contact may do work: A always positive B always negative C zero D infinite
Correct Answer: C for contact point instantaneously at rest.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
11. NEET Exam-style Question: Rotational kinetic energy is: A 1/2mv² B 1/2Iω² C Iω D τθ
Correct Answer: B. Krot=1/2Iω².
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
12. NEET Exam-style Question: Work done by constant torque τ through angle θ is: A τθ B τ/θ C θ/τ D Iω
Correct Answer: A.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
13. NEET Exam-style Question: Power in rotation equals: A Fv B τω C I/ω D τ/ω
Correct Answer: B.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
14. NEET Exam-style Question: Rotational analogue of F=ma is: A τ=Iα B L=Iω C v=Rω D W=τθ
Correct Answer: A.
Detailed Explanation: This tests dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
15. NEET Exam-style Question: Pure rolling condition is: A v=Rω B v=ω/R C a=ωR² D I=MR
Correct Answer: A.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
16. NEET Exam-style Question: Total KE of rolling body is: A translational only B rotational only C 1/2mv²+1/2Iω² D zero
Correct Answer: C.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
17. NEET Exam-style Question: Rolling KE of ring is: A 1/2mv² B mv² C 3/4mv² D 7/10mv²
Correct Answer: B.
Detailed Explanation: This tests ring rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests ring rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
18. NEET Exam-style Question: Rolling KE of solid disc/cylinder is: A mv² B 3/4mv² C 5/6mv² D 7/10mv²
Correct Answer: B.
Detailed Explanation: This tests disc rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests disc rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
19. NEET Exam-style Question: Which rolls fastest down same incline: ring, disc, solid sphere?
Correct Answer: Solid sphere, because I/MR² is smallest.
Detailed Explanation: This tests incline race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
20. NEET Exam-style Question: In pure rolling on fixed rough surface, static friction at contact may do work: A always positive B always negative C zero D infinite
Correct Answer: C for contact point instantaneously at rest.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
21. NEET Exam-style Question: Rotational kinetic energy is: A 1/2mv² B 1/2Iω² C Iω D τθ
Correct Answer: B. Krot=1/2Iω².
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
22. NEET Exam-style Question: Work done by constant torque τ through angle θ is: A τθ B τ/θ C θ/τ D Iω
Correct Answer: A.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
23. NEET Exam-style Question: Power in rotation equals: A Fv B τω C I/ω D τ/ω
Correct Answer: B.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
24. NEET Exam-style Question: Rotational analogue of F=ma is: A τ=Iα B L=Iω C v=Rω D W=τθ
Correct Answer: A.
Detailed Explanation: This tests dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
25. NEET Exam-style Question: Pure rolling condition is: A v=Rω B v=ω/R C a=ωR² D I=MR
Correct Answer: A.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
26. NEET Exam-style Question: Total KE of rolling body is: A translational only B rotational only C 1/2mv²+1/2Iω² D zero
Correct Answer: C.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
27. NEET Exam-style Question: Rolling KE of ring is: A 1/2mv² B mv² C 3/4mv² D 7/10mv²
Correct Answer: B.
Detailed Explanation: This tests ring rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests ring rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
28. NEET Exam-style Question: Rolling KE of solid disc/cylinder is: A mv² B 3/4mv² C 5/6mv² D 7/10mv²
Correct Answer: B.
Detailed Explanation: This tests disc rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests disc rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
29. NEET Exam-style Question: Which rolls fastest down same incline: ring, disc, solid sphere?
Correct Answer: Solid sphere, because I/MR² is smallest.
Detailed Explanation: This tests incline race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
30. NEET Exam-style Question: In pure rolling on fixed rough surface, static friction at contact may do work: A always positive B always negative C zero D infinite
Correct Answer: C for contact point instantaneously at rest.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
31. NEET Exam-style Question: Rotational kinetic energy is: A 1/2mv² B 1/2Iω² C Iω D τθ
Correct Answer: B. Krot=1/2Iω².
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
32. NEET Exam-style Question: Work done by constant torque τ through angle θ is: A τθ B τ/θ C θ/τ D Iω
Correct Answer: A.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
33. NEET Exam-style Question: Power in rotation equals: A Fv B τω C I/ω D τ/ω
Correct Answer: B.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
34. NEET Exam-style Question: Rotational analogue of F=ma is: A τ=Iα B L=Iω C v=Rω D W=τθ
Correct Answer: A.
Detailed Explanation: This tests dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
35. NEET Exam-style Question: Pure rolling condition is: A v=Rω B v=ω/R C a=ωR² D I=MR
Correct Answer: A.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
36. NEET Exam-style Question: Total KE of rolling body is: A translational only B rotational only C 1/2mv²+1/2Iω² D zero
Correct Answer: C.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
37. NEET Exam-style Question: Rolling KE of ring is: A 1/2mv² B mv² C 3/4mv² D 7/10mv²
Correct Answer: B.
Detailed Explanation: This tests ring rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests ring rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
38. NEET Exam-style Question: Rolling KE of solid disc/cylinder is: A mv² B 3/4mv² C 5/6mv² D 7/10mv²
Correct Answer: B.
Detailed Explanation: This tests disc rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests disc rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
39. NEET Exam-style Question: Which rolls fastest down same incline: ring, disc, solid sphere?
Correct Answer: Solid sphere, because I/MR² is smallest.
Detailed Explanation: This tests incline race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
40. NEET Exam-style Question: In pure rolling on fixed rough surface, static friction at contact may do work: A always positive B always negative C zero D infinite
Correct Answer: C for contact point instantaneously at rest.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
41. NEET Exam-style Question: Rotational kinetic energy is: A 1/2mv² B 1/2Iω² C Iω D τθ
Correct Answer: B. Krot=1/2Iω².
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
42. NEET Exam-style Question: Work done by constant torque τ through angle θ is: A τθ B τ/θ C θ/τ D Iω
Correct Answer: A.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
43. NEET Exam-style Question: Power in rotation equals: A Fv B τω C I/ω D τ/ω
Correct Answer: B.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
44. NEET Exam-style Question: Rotational analogue of F=ma is: A τ=Iα B L=Iω C v=Rω D W=τθ
Correct Answer: A.
Detailed Explanation: This tests dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
45. NEET Exam-style Question: Pure rolling condition is: A v=Rω B v=ω/R C a=ωR² D I=MR
Correct Answer: A.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
46. NEET Exam-style Question: Total KE of rolling body is: A translational only B rotational only C 1/2mv²+1/2Iω² D zero
Correct Answer: C.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
47. NEET Exam-style Question: Rolling KE of ring is: A 1/2mv² B mv² C 3/4mv² D 7/10mv²
Correct Answer: B.
Detailed Explanation: This tests ring rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests ring rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
48. NEET Exam-style Question: Rolling KE of solid disc/cylinder is: A mv² B 3/4mv² C 5/6mv² D 7/10mv²
Correct Answer: B.
Detailed Explanation: This tests disc rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests disc rolling. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
49. NEET Exam-style Question: Which rolls fastest down same incline: ring, disc, solid sphere?
Correct Answer: Solid sphere, because I/MR² is smallest.
Detailed Explanation: This tests incline race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
50. NEET Exam-style Question: In pure rolling on fixed rough surface, static friction at contact may do work: A always positive B always negative C zero D infinite
Correct Answer: C for contact point instantaneously at rest.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
15
JEE Main Question Bank
50 difficult JEE Main-style questions on rolling energy, τ=Iα, incline, power and friction.
1. JEE Main Exam-style Question: I=4 kg m² and ω=5 rad/s. Find Krot.
Correct Answer: K=1/2 Iω²=50 J.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
2. JEE Main Exam-style Question: Torque 10 N m turns wheel by 6 rad. Work?
Correct Answer: W=τθ=60 J.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
3. JEE Main Exam-style Question: Torque 20 N m acts at 30 rad/s. Power?
Correct Answer: P=τω=600 W.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
4. JEE Main Exam-style Question: Torque 12 N m on I=3 kg m². Find α.
Correct Answer: α=τ/I=4 rad/s².
Detailed Explanation: This tests tau I alpha. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests tau I alpha. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
5. JEE Main Exam-style Question: Wheel R=0.4 m has ω=20 rad/s. Centre speed?
Correct Answer: v=Rω=8 m/s.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
6. JEE Main Exam-style Question: Solid cylinder mass m speed v. Total KE?
Correct Answer: K=3/4mv².
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
7. JEE Main Exam-style Question: Ring rolls down incline. Acceleration?
Correct Answer: a=g sinθ/(1+1)=g sinθ/2.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
8. JEE Main Exam-style Question: Solid sphere rolls down incline. Acceleration?
Correct Answer: a=g sinθ/(1+2/5)=5g sinθ/7.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
9. JEE Main Exam-style Question: Pulley has nonzero I. Why acceleration is less?
Correct Answer: Some energy/torque goes into pulley rotation.
Detailed Explanation: This tests pulley. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests pulley. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
10. JEE Main Exam-style Question: In spool questions, main trap is:
Correct Answer: Direction of friction/rolling constraint depends on pull geometry.
Detailed Explanation: This tests spool. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests spool. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
11. JEE Main Exam-style Question: I=4 kg m² and ω=5 rad/s. Find Krot.
Correct Answer: K=1/2 Iω²=50 J.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
12. JEE Main Exam-style Question: Torque 10 N m turns wheel by 6 rad. Work?
Correct Answer: W=τθ=60 J.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
13. JEE Main Exam-style Question: Torque 20 N m acts at 30 rad/s. Power?
Correct Answer: P=τω=600 W.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
14. JEE Main Exam-style Question: Torque 12 N m on I=3 kg m². Find α.
Correct Answer: α=τ/I=4 rad/s².
Detailed Explanation: This tests tau I alpha. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests tau I alpha. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
15. JEE Main Exam-style Question: Wheel R=0.4 m has ω=20 rad/s. Centre speed?
Correct Answer: v=Rω=8 m/s.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
16. JEE Main Exam-style Question: Solid cylinder mass m speed v. Total KE?
Correct Answer: K=3/4mv².
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
17. JEE Main Exam-style Question: Ring rolls down incline. Acceleration?
Correct Answer: a=g sinθ/(1+1)=g sinθ/2.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
18. JEE Main Exam-style Question: Solid sphere rolls down incline. Acceleration?
Correct Answer: a=g sinθ/(1+2/5)=5g sinθ/7.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
19. JEE Main Exam-style Question: Pulley has nonzero I. Why acceleration is less?
Correct Answer: Some energy/torque goes into pulley rotation.
Detailed Explanation: This tests pulley. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests pulley. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
20. JEE Main Exam-style Question: In spool questions, main trap is:
Correct Answer: Direction of friction/rolling constraint depends on pull geometry.
Detailed Explanation: This tests spool. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests spool. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
21. JEE Main Exam-style Question: I=4 kg m² and ω=5 rad/s. Find Krot.
Correct Answer: K=1/2 Iω²=50 J.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
22. JEE Main Exam-style Question: Torque 10 N m turns wheel by 6 rad. Work?
Correct Answer: W=τθ=60 J.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
23. JEE Main Exam-style Question: Torque 20 N m acts at 30 rad/s. Power?
Correct Answer: P=τω=600 W.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
24. JEE Main Exam-style Question: Torque 12 N m on I=3 kg m². Find α.
Correct Answer: α=τ/I=4 rad/s².
Detailed Explanation: This tests tau I alpha. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests tau I alpha. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
25. JEE Main Exam-style Question: Wheel R=0.4 m has ω=20 rad/s. Centre speed?
Correct Answer: v=Rω=8 m/s.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
26. JEE Main Exam-style Question: Solid cylinder mass m speed v. Total KE?
Correct Answer: K=3/4mv².
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
27. JEE Main Exam-style Question: Ring rolls down incline. Acceleration?
Correct Answer: a=g sinθ/(1+1)=g sinθ/2.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
28. JEE Main Exam-style Question: Solid sphere rolls down incline. Acceleration?
Correct Answer: a=g sinθ/(1+2/5)=5g sinθ/7.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
29. JEE Main Exam-style Question: Pulley has nonzero I. Why acceleration is less?
Correct Answer: Some energy/torque goes into pulley rotation.
Detailed Explanation: This tests pulley. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests pulley. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
30. JEE Main Exam-style Question: In spool questions, main trap is:
Correct Answer: Direction of friction/rolling constraint depends on pull geometry.
Detailed Explanation: This tests spool. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests spool. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
31. JEE Main Exam-style Question: I=4 kg m² and ω=5 rad/s. Find Krot.
Correct Answer: K=1/2 Iω²=50 J.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
32. JEE Main Exam-style Question: Torque 10 N m turns wheel by 6 rad. Work?
Correct Answer: W=τθ=60 J.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
33. JEE Main Exam-style Question: Torque 20 N m acts at 30 rad/s. Power?
Correct Answer: P=τω=600 W.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
34. JEE Main Exam-style Question: Torque 12 N m on I=3 kg m². Find α.
Correct Answer: α=τ/I=4 rad/s².
Detailed Explanation: This tests tau I alpha. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests tau I alpha. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
35. JEE Main Exam-style Question: Wheel R=0.4 m has ω=20 rad/s. Centre speed?
Correct Answer: v=Rω=8 m/s.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
36. JEE Main Exam-style Question: Solid cylinder mass m speed v. Total KE?
Correct Answer: K=3/4mv².
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
37. JEE Main Exam-style Question: Ring rolls down incline. Acceleration?
Correct Answer: a=g sinθ/(1+1)=g sinθ/2.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
38. JEE Main Exam-style Question: Solid sphere rolls down incline. Acceleration?
Correct Answer: a=g sinθ/(1+2/5)=5g sinθ/7.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
39. JEE Main Exam-style Question: Pulley has nonzero I. Why acceleration is less?
Correct Answer: Some energy/torque goes into pulley rotation.
Detailed Explanation: This tests pulley. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests pulley. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
40. JEE Main Exam-style Question: In spool questions, main trap is:
Correct Answer: Direction of friction/rolling constraint depends on pull geometry.
Detailed Explanation: This tests spool. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests spool. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
41. JEE Main Exam-style Question: I=4 kg m² and ω=5 rad/s. Find Krot.
Correct Answer: K=1/2 Iω²=50 J.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rotational KE. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
42. JEE Main Exam-style Question: Torque 10 N m turns wheel by 6 rad. Work?
Correct Answer: W=τθ=60 J.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests work rotation. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
43. JEE Main Exam-style Question: Torque 20 N m acts at 30 rad/s. Power?
Correct Answer: P=τω=600 W.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests power. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
44. JEE Main Exam-style Question: Torque 12 N m on I=3 kg m². Find α.
Correct Answer: α=τ/I=4 rad/s².
Detailed Explanation: This tests tau I alpha. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests tau I alpha. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
45. JEE Main Exam-style Question: Wheel R=0.4 m has ω=20 rad/s. Centre speed?
Correct Answer: v=Rω=8 m/s.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling condition. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
46. JEE Main Exam-style Question: Solid cylinder mass m speed v. Total KE?
Correct Answer: K=3/4mv².
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling energy. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
47. JEE Main Exam-style Question: Ring rolls down incline. Acceleration?
Correct Answer: a=g sinθ/(1+1)=g sinθ/2.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
48. JEE Main Exam-style Question: Solid sphere rolls down incline. Acceleration?
Correct Answer: a=g sinθ/(1+2/5)=5g sinθ/7.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
49. JEE Main Exam-style Question: Pulley has nonzero I. Why acceleration is less?
Correct Answer: Some energy/torque goes into pulley rotation.
Detailed Explanation: This tests pulley. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests pulley. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
50. JEE Main Exam-style Question: In spool questions, main trap is:
Correct Answer: Direction of friction/rolling constraint depends on pull geometry.
Detailed Explanation: This tests spool. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests spool. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
16
JEE Advanced Question Bank
50 advanced questions on constraints, spools, pulleys, slipping and graph-based rotational dynamics.
1. JEE Advanced Exam-style Question: A rolling disc has v=Rω. Differentiate to get relation between accelerations.
Correct Answer: a=Rα for pure rolling.
Detailed Explanation: This tests rolling constraints. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling constraints. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
2. JEE Advanced Exam-style Question: Why can a pulled spool move toward or away from pull?
Correct Answer: Torque about contact depends on line of action and inner/outer radii.
Detailed Explanation: This tests spool problems. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests spool problems. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
3. JEE Advanced Exam-style Question: For string not slipping on pulley, what constraint links a and α?
Correct Answer: a=Rα.
Detailed Explanation: This tests pulley with moment of inertia. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests pulley with moment of inertia. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
4. JEE Advanced Exam-style Question: Can use v=Rω during slipping?
Correct Answer: No, v=Rω only for pure rolling.
Detailed Explanation: This tests rolling with slipping. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling with slipping. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
5. JEE Advanced Exam-style Question: A torque τ acts through θ on body I from rest. Find ω.
Correct Answer: τθ=1/2Iω², so ω=sqrt(2τθ/I).
Detailed Explanation: This tests energy + torque. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests energy + torque. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
6. JEE Advanced Exam-style Question: Area under τ-θ graph gives:
Correct Answer: Rotational work.
Detailed Explanation: This tests graph dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests graph dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
7. JEE Advanced Exam-style Question: Derive a for rolling body.
Correct Answer: Use mg sinθ - f=ma and fR=Iα with a=Rα, giving a=g sinθ/(1+I/MR²).
Detailed Explanation: This tests rolling incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
8. JEE Advanced Exam-style Question: Why solid sphere beats ring down incline?
Correct Answer: Smaller I/MR² means larger acceleration.
Detailed Explanation: This tests race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
9. JEE Advanced Exam-style Question: For ring rolling, rotational KE fraction of total?
Correct Answer: Half; Ktrans=Krot=1/2mv².
Detailed Explanation: This tests energy split. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests energy split. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
10. JEE Advanced Exam-style Question: When does static friction do zero work in pure rolling?
Correct Answer: On fixed surface because contact point is instantaneously at rest.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
11. JEE Advanced Exam-style Question: A rolling disc has v=Rω. Differentiate to get relation between accelerations.
Correct Answer: a=Rα for pure rolling.
Detailed Explanation: This tests rolling constraints. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling constraints. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
12. JEE Advanced Exam-style Question: Why can a pulled spool move toward or away from pull?
Correct Answer: Torque about contact depends on line of action and inner/outer radii.
Detailed Explanation: This tests spool problems. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests spool problems. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
13. JEE Advanced Exam-style Question: For string not slipping on pulley, what constraint links a and α?
Correct Answer: a=Rα.
Detailed Explanation: This tests pulley with moment of inertia. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests pulley with moment of inertia. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
14. JEE Advanced Exam-style Question: Can use v=Rω during slipping?
Correct Answer: No, v=Rω only for pure rolling.
Detailed Explanation: This tests rolling with slipping. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling with slipping. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
15. JEE Advanced Exam-style Question: A torque τ acts through θ on body I from rest. Find ω.
Correct Answer: τθ=1/2Iω², so ω=sqrt(2τθ/I).
Detailed Explanation: This tests energy + torque. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests energy + torque. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
16. JEE Advanced Exam-style Question: Area under τ-θ graph gives:
Correct Answer: Rotational work.
Detailed Explanation: This tests graph dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests graph dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
17. JEE Advanced Exam-style Question: Derive a for rolling body.
Correct Answer: Use mg sinθ - f=ma and fR=Iα with a=Rα, giving a=g sinθ/(1+I/MR²).
Detailed Explanation: This tests rolling incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
18. JEE Advanced Exam-style Question: Why solid sphere beats ring down incline?
Correct Answer: Smaller I/MR² means larger acceleration.
Detailed Explanation: This tests race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
19. JEE Advanced Exam-style Question: For ring rolling, rotational KE fraction of total?
Correct Answer: Half; Ktrans=Krot=1/2mv².
Detailed Explanation: This tests energy split. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests energy split. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
20. JEE Advanced Exam-style Question: When does static friction do zero work in pure rolling?
Correct Answer: On fixed surface because contact point is instantaneously at rest.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
21. JEE Advanced Exam-style Question: A rolling disc has v=Rω. Differentiate to get relation between accelerations.
Correct Answer: a=Rα for pure rolling.
Detailed Explanation: This tests rolling constraints. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling constraints. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
22. JEE Advanced Exam-style Question: Why can a pulled spool move toward or away from pull?
Correct Answer: Torque about contact depends on line of action and inner/outer radii.
Detailed Explanation: This tests spool problems. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests spool problems. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
23. JEE Advanced Exam-style Question: For string not slipping on pulley, what constraint links a and α?
Correct Answer: a=Rα.
Detailed Explanation: This tests pulley with moment of inertia. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests pulley with moment of inertia. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
24. JEE Advanced Exam-style Question: Can use v=Rω during slipping?
Correct Answer: No, v=Rω only for pure rolling.
Detailed Explanation: This tests rolling with slipping. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling with slipping. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
25. JEE Advanced Exam-style Question: A torque τ acts through θ on body I from rest. Find ω.
Correct Answer: τθ=1/2Iω², so ω=sqrt(2τθ/I).
Detailed Explanation: This tests energy + torque. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests energy + torque. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
26. JEE Advanced Exam-style Question: Area under τ-θ graph gives:
Correct Answer: Rotational work.
Detailed Explanation: This tests graph dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests graph dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
27. JEE Advanced Exam-style Question: Derive a for rolling body.
Correct Answer: Use mg sinθ - f=ma and fR=Iα with a=Rα, giving a=g sinθ/(1+I/MR²).
Detailed Explanation: This tests rolling incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
28. JEE Advanced Exam-style Question: Why solid sphere beats ring down incline?
Correct Answer: Smaller I/MR² means larger acceleration.
Detailed Explanation: This tests race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
29. JEE Advanced Exam-style Question: For ring rolling, rotational KE fraction of total?
Correct Answer: Half; Ktrans=Krot=1/2mv².
Detailed Explanation: This tests energy split. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests energy split. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
30. JEE Advanced Exam-style Question: When does static friction do zero work in pure rolling?
Correct Answer: On fixed surface because contact point is instantaneously at rest.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
31. JEE Advanced Exam-style Question: A rolling disc has v=Rω. Differentiate to get relation between accelerations.
Correct Answer: a=Rα for pure rolling.
Detailed Explanation: This tests rolling constraints. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling constraints. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
32. JEE Advanced Exam-style Question: Why can a pulled spool move toward or away from pull?
Correct Answer: Torque about contact depends on line of action and inner/outer radii.
Detailed Explanation: This tests spool problems. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests spool problems. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
33. JEE Advanced Exam-style Question: For string not slipping on pulley, what constraint links a and α?
Correct Answer: a=Rα.
Detailed Explanation: This tests pulley with moment of inertia. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests pulley with moment of inertia. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
34. JEE Advanced Exam-style Question: Can use v=Rω during slipping?
Correct Answer: No, v=Rω only for pure rolling.
Detailed Explanation: This tests rolling with slipping. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling with slipping. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
35. JEE Advanced Exam-style Question: A torque τ acts through θ on body I from rest. Find ω.
Correct Answer: τθ=1/2Iω², so ω=sqrt(2τθ/I).
Detailed Explanation: This tests energy + torque. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests energy + torque. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
36. JEE Advanced Exam-style Question: Area under τ-θ graph gives:
Correct Answer: Rotational work.
Detailed Explanation: This tests graph dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests graph dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
37. JEE Advanced Exam-style Question: Derive a for rolling body.
Correct Answer: Use mg sinθ - f=ma and fR=Iα with a=Rα, giving a=g sinθ/(1+I/MR²).
Detailed Explanation: This tests rolling incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
38. JEE Advanced Exam-style Question: Why solid sphere beats ring down incline?
Correct Answer: Smaller I/MR² means larger acceleration.
Detailed Explanation: This tests race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
39. JEE Advanced Exam-style Question: For ring rolling, rotational KE fraction of total?
Correct Answer: Half; Ktrans=Krot=1/2mv².
Detailed Explanation: This tests energy split. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests energy split. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
40. JEE Advanced Exam-style Question: When does static friction do zero work in pure rolling?
Correct Answer: On fixed surface because contact point is instantaneously at rest.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
41. JEE Advanced Exam-style Question: A rolling disc has v=Rω. Differentiate to get relation between accelerations.
Correct Answer: a=Rα for pure rolling.
Detailed Explanation: This tests rolling constraints. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling constraints. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
42. JEE Advanced Exam-style Question: Why can a pulled spool move toward or away from pull?
Correct Answer: Torque about contact depends on line of action and inner/outer radii.
Detailed Explanation: This tests spool problems. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests spool problems. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
43. JEE Advanced Exam-style Question: For string not slipping on pulley, what constraint links a and α?
Correct Answer: a=Rα.
Detailed Explanation: This tests pulley with moment of inertia. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests pulley with moment of inertia. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
44. JEE Advanced Exam-style Question: Can use v=Rω during slipping?
Correct Answer: No, v=Rω only for pure rolling.
Detailed Explanation: This tests rolling with slipping. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling with slipping. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
45. JEE Advanced Exam-style Question: A torque τ acts through θ on body I from rest. Find ω.
Correct Answer: τθ=1/2Iω², so ω=sqrt(2τθ/I).
Detailed Explanation: This tests energy + torque. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests energy + torque. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
46. JEE Advanced Exam-style Question: Area under τ-θ graph gives:
Correct Answer: Rotational work.
Detailed Explanation: This tests graph dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests graph dynamics. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
47. JEE Advanced Exam-style Question: Derive a for rolling body.
Correct Answer: Use mg sinθ - f=ma and fR=Iα with a=Rα, giving a=g sinθ/(1+I/MR²).
Detailed Explanation: This tests rolling incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests rolling incline. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
48. JEE Advanced Exam-style Question: Why solid sphere beats ring down incline?
Correct Answer: Smaller I/MR² means larger acceleration.
Detailed Explanation: This tests race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests race. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
49. JEE Advanced Exam-style Question: For ring rolling, rotational KE fraction of total?
Correct Answer: Half; Ktrans=Krot=1/2mv².
Detailed Explanation: This tests energy split. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests energy split. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
50. JEE Advanced Exam-style Question: When does static friction do zero work in pure rolling?
Correct Answer: On fixed surface because contact point is instantaneously at rest.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
Detailed Explanation: This tests friction. Use energy, torque equation, or rolling constraint based on what is given. For pure rolling, use v=Rω and a=Rα; for slipping, do not use these constraints blindly.
17
IB / IGCSE / A-Level Questions
Separate international banks with answers and explanations.
IB Questions
IB 1. Define rotational kinetic energy.
Energy due to rotation: K=1/2Iω².
IB 2. Work done by torque.
W=τθ for constant torque.
IB 3. Variable torque work.
W=∫τdθ.
IB 4. Power in rotation.
P=τω.
IB 5. Rotational dynamics relation.
τ=Iα.
IB 6. Pure rolling condition.
v=Rω.
IB 7. Acceleration condition in pure rolling.
a=Rα.
IB 8. Total rolling KE.
1/2mv²+1/2Iω².
IB 9. Ring rolling KE.
mv².
IB 10. Disc rolling KE.
3/4mv².
IB 11. Solid sphere rolling KE.
7/10mv².
IB 12. Hollow sphere rolling KE.
5/6mv².
IB 13. Rolling incline acceleration.
g sinθ/(1+I/MR²).
IB 14. Velocity after height h.
sqrt[2gh/(1+I/MR²)].
IB 15. Static friction in pure rolling.
May provide torque without doing work on fixed surface.
IB 16. Kinetic friction occurs in.
Slipping.
IB 17. Top point speed in rolling wheel.
2v relative to ground.
IB 18. Bottom point speed in pure rolling.
Zero.
IB 19. Centre point speed.
v.
IB 20. Instantaneous axis of rotation.
Contact point in pure rolling.
IB 21. Fan motor uses.
Rotational power.
IB 22. Flywheel stores.
Rotational kinetic energy.
IB 23. Pulley with I changes acceleration because.
Some torque accelerates rotation.
IB 24. Yo-yo combines.
Translation and rotation.
IB 25. Rolling race depends on.
I/MR², not mass alone.
IGCSE Questions
IGCSE 1. What is rolling motion?
Combination of translation and rotation.
IGCSE 2. Pure rolling condition.
v=Rω.
IGCSE 3. Bottom point speed in pure rolling.
Zero.
IGCSE 4. Top point speed.
Twice centre speed.
IGCSE 5. Rotational kinetic energy formula.
1/2Iω².
IGCSE 6. Total rolling energy includes.
Translational and rotational energy.
IGCSE 7. Work by torque formula.
W=τθ.
IGCSE 8. Power in rotation.
P=τω.
IGCSE 9. Torque causes angular.
Acceleration.
IGCSE 10. Formula τ=Iα means.
Torque equals moment of inertia times angular acceleration.
IGCSE 11. A ring or solid sphere rolls faster?
Solid sphere.
IGCSE 12. Why solid sphere faster than ring?
Smaller moment of inertia factor.
IGCSE 13. Friction in pure rolling is.
Static friction.
IGCSE 14. Slipping uses which friction?
Kinetic friction.
IGCSE 15. Rolling wheel centre moves with.
Translational speed.
IGCSE 16. Car tyre motion is.
Rolling motion.
IGCSE 17. Bowling ball has.
Translation plus rotation.
IGCSE 18. Flywheel stores energy by.
Rotation.
IGCSE 19. Fan motor gives rotational.
Power.
IGCSE 20. Velocity after height h depends on.
I/MR².
IGCSE 21. Heavier body always rolls faster?
No.
IGCSE 22. Moment of inertia affects rolling?
Yes.
IGCSE 23. Wheel radius links v and.
ω.
IGCSE 24. Angular acceleration links to linear.
a=Rα.
IGCSE 25. Do not use v=Rω when.
Slipping.
A-Level Questions
A-Level 1. Derive rotational work element.
dW=τdθ.
A-Level 2. Area under torque-angle graph.
Work done.
A-Level 3. Rotational power derivation.
P=dW/dt=τdθ/dt=τω.
A-Level 4. Derive rolling KE expression.
K=1/2Mv²+1/2Iω².
A-Level 5. Use pure rolling to rewrite KE.
K=1/2Mv²[1+I/(MR²)].
A-Level 6. Ring rolling energy.
mv².
A-Level 7. Disc rolling energy.
3/4Mv².
A-Level 8. Solid sphere rolling energy.
7/10Mv².
A-Level 9. Hollow sphere rolling energy.
5/6Mv².
A-Level 10. Incline acceleration derivation key.
Combine translation, rotation and a=Rα.
A-Level 11. Friction role on incline.
Provides torque for rolling.
A-Level 12. Static friction work in pure rolling fixed surface.
Zero total work at contact.
A-Level 13. Slipping condition.
v≠Rω.
A-Level 14. Instantaneous centre.
Point of contact.
A-Level 15. Pulley constraint.
a=Rα if string does not slip.
A-Level 16. Yo-yo energy.
Potential converts to translational plus rotational KE.
A-Level 17. Spool direction depends on.
Torque about contact point.
A-Level 18. Rolling race ranking.
Smaller I/MR² reaches first.
A-Level 19. Solid sphere acceleration.
5g sinθ/7.
A-Level 20. Disc acceleration.
2g sinθ/3.
A-Level 21. Ring acceleration.
g sinθ/2.
A-Level 22. Power graph connection.
P=dK/dt.
A-Level 23. Rotational KE vs omega graph.
Parabola.
A-Level 24. Torque-angle graph area units.
Joule.
A-Level 25. Friction mistake in pure rolling.
Assuming kinetic friction acts.
18
Assertion Reason
30 assertion-reason questions.
1. Assertion: Rolling motion is translation plus rotation. Reason: Centre of mass translates while body rotates about COM.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
2. Assertion: Pure rolling condition is v=Rω. Reason: Contact point has zero velocity relative to ground.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
3. Assertion: Total rolling KE is only 1/2mv². Reason: Rolling body also rotates.
Answer: Assertion false; reason true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
4. Assertion: Static friction may do zero work in pure rolling. Reason: Contact point is instantaneously at rest on fixed surface.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
5. Assertion: Ring rolls slower than solid sphere down incline. Reason: Ring has larger I/MR².
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
6. Assertion: Power in rotation is τω. Reason: P=dW/dt and dW=τdθ.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
7. Assertion: Area under τ-θ graph is work. Reason: dW=τdθ.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
8. Assertion: During slipping, v=Rω must be used. Reason: Slipping means contact point has relative motion.
Answer: Assertion false; reason true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
9. Assertion: τ=Iα is rotational analogue of F=ma. Reason: I plays role of rotational inertia.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
10. Assertion: Heavier body always reaches first in rolling race. Reason: Acceleration depends on I/MR².
Answer: Assertion false; reason true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
11. Assertion: Rolling motion is translation plus rotation. Reason: Centre of mass translates while body rotates about COM.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
12. Assertion: Pure rolling condition is v=Rω. Reason: Contact point has zero velocity relative to ground.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
13. Assertion: Total rolling KE is only 1/2mv². Reason: Rolling body also rotates.
Answer: Assertion false; reason true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
14. Assertion: Static friction may do zero work in pure rolling. Reason: Contact point is instantaneously at rest on fixed surface.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
15. Assertion: Ring rolls slower than solid sphere down incline. Reason: Ring has larger I/MR².
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
16. Assertion: Power in rotation is τω. Reason: P=dW/dt and dW=τdθ.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
17. Assertion: Area under τ-θ graph is work. Reason: dW=τdθ.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
18. Assertion: During slipping, v=Rω must be used. Reason: Slipping means contact point has relative motion.
Answer: Assertion false; reason true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
19. Assertion: τ=Iα is rotational analogue of F=ma. Reason: I plays role of rotational inertia.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
20. Assertion: Heavier body always reaches first in rolling race. Reason: Acceleration depends on I/MR².
Answer: Assertion false; reason true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
21. Assertion: Rolling motion is translation plus rotation. Reason: Centre of mass translates while body rotates about COM.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
22. Assertion: Pure rolling condition is v=Rω. Reason: Contact point has zero velocity relative to ground.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
23. Assertion: Total rolling KE is only 1/2mv². Reason: Rolling body also rotates.
Answer: Assertion false; reason true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
24. Assertion: Static friction may do zero work in pure rolling. Reason: Contact point is instantaneously at rest on fixed surface.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
25. Assertion: Ring rolls slower than solid sphere down incline. Reason: Ring has larger I/MR².
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
26. Assertion: Power in rotation is τω. Reason: P=dW/dt and dW=τdθ.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
27. Assertion: Area under τ-θ graph is work. Reason: dW=τdθ.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
28. Assertion: During slipping, v=Rω must be used. Reason: Slipping means contact point has relative motion.
Answer: Assertion false; reason true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
29. Assertion: τ=Iα is rotational analogue of F=ma. Reason: I plays role of rotational inertia.
Answer: Both true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
30. Assertion: Heavier body always reaches first in rolling race. Reason: Acceleration depends on I/MR².
Answer: Assertion false; reason true.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
Explanation: First decide whether motion is pure rolling or slipping, then choose the correct constraint and energy equation.
19
Case Study Questions
Rolling race, tyre, flywheel, yo-yo, bowling ball and cylinder incline cases.
Case Study: Rolling race
Passage: Ring, disc and solid sphere roll from same height. Questions: acceleration, velocity, arrival order, role of mass distribution and energy split.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: Solid sphere reaches first, then disc/cylinder, then ring. Smaller I/MR² gives larger acceleration.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: Solid sphere reaches first, then disc/cylinder, then ring. Smaller I/MR² gives larger acceleration.
Case Study: Car tyre rolling
Passage: A tyre rolls without slipping on road. Questions: contact velocity, friction type, top point velocity and v=Rω.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: Contact point is instantaneously at rest; top point speed is 2v.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: Contact point is instantaneously at rest; top point speed is 2v.
Case Study: Flywheel
Passage: A flywheel stores energy while spinning. Questions: Krot, power, torque and why large I helps.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: K=1/2Iω² and P=τω; larger I stores more energy at same omega.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: K=1/2Iω² and P=τω; larger I stores more energy at same omega.
Case Study: Yo-yo
Passage: A yo-yo descends while unwinding. Questions: energy forms, torque, constraint and acceleration.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: Potential energy splits into translational and rotational KE.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: Potential energy splits into translational and rotational KE.
Case Study: Bowling ball
Passage: A bowling ball initially slips then rolls. Questions: kinetic friction, rolling condition and energy loss.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: During slipping, kinetic friction acts; pure rolling begins when v=Rω.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: During slipping, kinetic friction acts; pure rolling begins when v=Rω.
Case Study: Cylinder rolling down incline
Passage: A solid cylinder rolls down a rough incline. Questions: acceleration, friction role, energy and final speed.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: Use a=2g sinθ/3 and K=3/4Mv² for solid cylinder.
Questions: Identify constraint, energy terms, friction type and formula.
Answers and Detailed Explanation: Use a=2g sinθ/3 and K=3/4Mv² for solid cylinder.
20
Common Student Mistakes
Avoid these before NEET/JEE rolling questions.
Forgetting Krot
Rolling energy is not only 1/2mv².
Pure Rolling vs Slipping
Use v=Rω only for pure rolling.
Wrong Friction Direction
Direction depends on tendency of slipping.
Wrong Moment of Inertia
Ring, disc, sphere and cylinder have different I.
Heavier Wins Myth
Race depends on I/MR², not mass alone.
Bad Energy Use
When slipping friction dissipates energy, simple conservation may fail.
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