System of Particles and Rotation Formula Sheet & PYQs

Searching for a Physics Tutor? If Centre of Mass, Momentum, Torque, Angular Momentum, Moment of Inertia or Rolling Motion is not clear, contact Kumar Sir.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar SirVisit WebsiteEmail Kumar Sir
ΣR
Class 11 Physics - Rotation Revision

system of particles and rotation formulas pyqs

Complete revision page with formulas, NCERT questions, PYQs and quick revision notes for rotational mechanics.

01

Complete Formula Sheet

Master table for the whole System of Particles and Rotation chapter.

TopicCore FormulaExam Use
COMrcm=Σmiri/ΣmiSystem position
Momentump=mv, J=ΔpCollision, impulse, recoil
Rocketv=u ln(M0/M)Variable mass
Torqueτ=r×F=rF sinθ=FdTurning effect
Coupleτ=F × separationZero net force, nonzero torque
Angular momentumL=r×p=IωRotational momentum
Conservation LI1ω1=I2ω2Zero external torque
MOII=Σmr²=∫r²dmMass distribution
Axis theoremI=Icm+Md², Iz=Ix+IyShifted axes, lamina
RollingK=1/2Mv²+1/2Iω², v=RωPure rolling energy
02

Centre of Mass Formulae

COMxcm=Σmx/Σmycm=Σmy/Σmzcm=Σmz/Σm
vcm=Σmv/Σmacm=Σma/ΣmFext=Macm
xcm=(MFxF-MRxR)/(MF-MR)ycm=(MFyF-MRyR)/(MF-MR)zcm=(MFzF-MRzR)/(MF-MR)
03

Momentum Formulae

p=mvp=mvJ=Δp=∫Fdt
Σpbefore=ΣpafterMV=mv
v=u ln(M0/M)

Explosion at rest: vector sum of final momenta is zero.

04

Torque Formulae

tau = r x Fτ=r×Fτ=rF sinθτ=Fd
Couple τ=F × separationW=τθ
P=τω

Moment arm is perpendicular distance from pivot to line of action.

05

Angular Momentum Formulae

QuantityFormulaTip
Particle LL=r×p=rp sinθUse perpendicular momentum component
Rigid body LL=IωFixed axis
Torque relationτ=dL/dtTorque changes L
ConservationI1ω1=I2ω2External torque zero
06

Moment of Inertia Formulae

ObjectAxisI
RodCentreML²/12
RodEndML²/3
RingCentreMR²
RingDiameterMR²/2
DiscCentreMR²/2
DiscDiameterMR²/4
DiscTangent3MR²/2
Solid cylinderAxisMR²/2
Hollow cylinderAxisMR²
Thick hollow cylinderAxis1/2M(R1²+R2²)
Solid sphereDiameter2MR²/5
Hollow sphereDiameter2MR²/3
I=Mk², I=Icm+Md², Iz=Ix+Iy
07

Rolling Motion Formulae

v = R omegav=Rωa=RαK=1/2Mv²+1/2Iω²a=g sinθ/(1+I/MR²)v=√[2gh/(1+I/MR²)]
BodyIKrolling
RingMR²Mv²
Disc/CylinderMR²/23/4Mv²
Solid sphere2MR²/57/10Mv²
Hollow sphere2MR²/35/6Mv²
08

NCERT Examples

NCERT Example: COM of two masses
COMSolution: 2 kg at 0 and 3 kg at 10 m. xcm=6 m.
Exam Tip: Identify the topic formula before substituting.
NCERT Example: recoil
p=mvSolution: Use m bullet v bullet = M gun V gun.
Exam Tip: Identify the topic formula before substituting.
NCERT Example: torque
tau = r x FSolution: Moment = force x perpendicular distance.
Exam Tip: Identify the topic formula before substituting.
NCERT Example: angular momentum
tau = r x FSolution: For fixed axis L=Iomega.
Exam Tip: Identify the topic formula before substituting.
NCERT Example: MOI
I = Sigma mr²Solution: Rod centre I=ML²/12.
Exam Tip: Identify the topic formula before substituting.
NCERT Example: rolling
v = R omegaSolution: K=1/2Mv²+1/2Iomega².
Exam Tip: Identify the topic formula before substituting.
09

NCERT Exercises

NCERT Exercise 1: NCERT Example: COM of two masses
COMAnswer: 2 kg at 0 and 3 kg at 10 m. xcm=6 m.
NCERT Exercise 2: NCERT Example: recoil
p=mvAnswer: Use m bullet v bullet = M gun V gun.
NCERT Exercise 3: NCERT Example: torque
tau = r x FAnswer: Moment = force x perpendicular distance.
NCERT Exercise 4: NCERT Example: angular momentum
tau = r x FAnswer: For fixed axis L=Iomega.
NCERT Exercise 5: NCERT Example: MOI
I = Sigma mr²Answer: Rod centre I=ML²/12.
NCERT Exercise 6: NCERT Example: rolling
v = R omegaAnswer: K=1/2Mv²+1/2Iomega².
NCERT Exercise 7: NCERT Example: COM of two masses
COMAnswer: 2 kg at 0 and 3 kg at 10 m. xcm=6 m.
NCERT Exercise 8: NCERT Example: recoil
p=mvAnswer: Use m bullet v bullet = M gun V gun.
NCERT Exercise 9: NCERT Example: torque
tau = r x FAnswer: Moment = force x perpendicular distance.
NCERT Exercise 10: NCERT Example: angular momentum
tau = r x FAnswer: For fixed axis L=Iomega.
NCERT Exercise 11: NCERT Example: MOI
I = Sigma mr²Answer: Rod centre I=ML²/12.
NCERT Exercise 12: NCERT Example: rolling
v = R omegaAnswer: K=1/2Mv²+1/2Iomega².
10

CBSE PYQs

CBSE board-style question 1: NCERT Example: COM of two masses
COMAnswer: 2 kg at 0 and 3 kg at 10 m. xcm=6 m.
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 2: NCERT Example: recoil
p=mvAnswer: Use m bullet v bullet = M gun V gun.
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 3: NCERT Example: torque
tau = r x FAnswer: Moment = force x perpendicular distance.
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 4: NCERT Example: angular momentum
tau = r x FAnswer: For fixed axis L=Iomega.
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 5: NCERT Example: MOI
I = Sigma mr²Answer: Rod centre I=ML²/12.
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 6: NCERT Example: rolling
v = R omegaAnswer: K=1/2Mv²+1/2Iomega².
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 7: NCERT Example: COM of two masses
COMAnswer: 2 kg at 0 and 3 kg at 10 m. xcm=6 m.
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 8: NCERT Example: recoil
p=mvAnswer: Use m bullet v bullet = M gun V gun.
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 9: NCERT Example: torque
tau = r x FAnswer: Moment = force x perpendicular distance.
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 10: NCERT Example: angular momentum
tau = r x FAnswer: For fixed axis L=Iomega.
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 11: NCERT Example: MOI
I = Sigma mr²Answer: Rod centre I=ML²/12.
Board Tip: Write formula, substitution and final unit.
CBSE board-style question 12: NCERT Example: rolling
v = R omegaAnswer: K=1/2Mv²+1/2Iomega².
Board Tip: Write formula, substitution and final unit.
11

NEET PYQs

50 NEET-style MCQs. Authentic years are not invented.

1. NEET Exam-style Question: Two equal masses are at x=0 and x=8 m. COM is: A 0 B 4 C 8 D 16
COMCorrect Answer: B. Equal masses give midpoint.
Detailed Explanation: This is a rotation revision problem from COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
2. NEET Exam-style Question: Momentum of 2 kg body moving at 5 m/s is: A 5 B 7 C 10 D 20
p=mvCorrect Answer: C. p=mv=10 kg m/s.
Detailed Explanation: This is a rotation revision problem from Momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
3. NEET Exam-style Question: Torque is maximum when angle between r and F is: A 0 B 45 C 90 D 180
tau = r x FCorrect Answer: C. tau=rF sin theta.
Detailed Explanation: This is a rotation revision problem from Torque. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
4. NEET Exam-style Question: For rigid body L equals: A Iomega B mr C Fd D P/t
tau = r x FCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Angular momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
5. NEET Exam-style Question: Moment of inertia of ring about central axis is: A MR² B MR²/2 C MR²/4 D 2MR²/5
I = Sigma mr²Correct Answer: A.
Detailed Explanation: This is a rotation revision problem from MOI. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
6. NEET Exam-style Question: Pure rolling condition is: A v=Romega B v=omega/R C a=omegaR D I=MR
v = R omegaCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Rolling. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
7. NEET Exam-style Question: Impulse equals: A Delta p B power C torque D energy
p=mvCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Impulse. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
8. NEET Exam-style Question: Rocket equation contains: A ln(M0/M) B sin theta C kx D MR²/2
p=mvCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Rocket. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
9. NEET Exam-style Question: If external torque is zero, conserved quantity is: A L B force C power D pressure
tau = r x FCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Conservation L. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
10. NEET Exam-style Question: Fastest among ring, disc, solid sphere on incline is:
v = R omegaCorrect Answer: Solid sphere because I/MR² is smallest.
Detailed Explanation: This is a rotation revision problem from Rolling race. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
11. NEET Exam-style Question: Two equal masses are at x=0 and x=8 m. COM is: A 0 B 4 C 8 D 16
COMCorrect Answer: B. Equal masses give midpoint.
Detailed Explanation: This is a rotation revision problem from COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
12. NEET Exam-style Question: Momentum of 2 kg body moving at 5 m/s is: A 5 B 7 C 10 D 20
p=mvCorrect Answer: C. p=mv=10 kg m/s.
Detailed Explanation: This is a rotation revision problem from Momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
13. NEET Exam-style Question: Torque is maximum when angle between r and F is: A 0 B 45 C 90 D 180
tau = r x FCorrect Answer: C. tau=rF sin theta.
Detailed Explanation: This is a rotation revision problem from Torque. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
14. NEET Exam-style Question: For rigid body L equals: A Iomega B mr C Fd D P/t
tau = r x FCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Angular momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
15. NEET Exam-style Question: Moment of inertia of ring about central axis is: A MR² B MR²/2 C MR²/4 D 2MR²/5
I = Sigma mr²Correct Answer: A.
Detailed Explanation: This is a rotation revision problem from MOI. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
16. NEET Exam-style Question: Pure rolling condition is: A v=Romega B v=omega/R C a=omegaR D I=MR
v = R omegaCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Rolling. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
17. NEET Exam-style Question: Impulse equals: A Delta p B power C torque D energy
p=mvCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Impulse. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
18. NEET Exam-style Question: Rocket equation contains: A ln(M0/M) B sin theta C kx D MR²/2
p=mvCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Rocket. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
19. NEET Exam-style Question: If external torque is zero, conserved quantity is: A L B force C power D pressure
tau = r x FCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Conservation L. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
20. NEET Exam-style Question: Fastest among ring, disc, solid sphere on incline is:
v = R omegaCorrect Answer: Solid sphere because I/MR² is smallest.
Detailed Explanation: This is a rotation revision problem from Rolling race. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
21. NEET Exam-style Question: Two equal masses are at x=0 and x=8 m. COM is: A 0 B 4 C 8 D 16
COMCorrect Answer: B. Equal masses give midpoint.
Detailed Explanation: This is a rotation revision problem from COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
22. NEET Exam-style Question: Momentum of 2 kg body moving at 5 m/s is: A 5 B 7 C 10 D 20
p=mvCorrect Answer: C. p=mv=10 kg m/s.
Detailed Explanation: This is a rotation revision problem from Momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
23. NEET Exam-style Question: Torque is maximum when angle between r and F is: A 0 B 45 C 90 D 180
tau = r x FCorrect Answer: C. tau=rF sin theta.
Detailed Explanation: This is a rotation revision problem from Torque. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
24. NEET Exam-style Question: For rigid body L equals: A Iomega B mr C Fd D P/t
tau = r x FCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Angular momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
25. NEET Exam-style Question: Moment of inertia of ring about central axis is: A MR² B MR²/2 C MR²/4 D 2MR²/5
I = Sigma mr²Correct Answer: A.
Detailed Explanation: This is a rotation revision problem from MOI. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
26. NEET Exam-style Question: Pure rolling condition is: A v=Romega B v=omega/R C a=omegaR D I=MR
v = R omegaCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Rolling. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
27. NEET Exam-style Question: Impulse equals: A Delta p B power C torque D energy
p=mvCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Impulse. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
28. NEET Exam-style Question: Rocket equation contains: A ln(M0/M) B sin theta C kx D MR²/2
p=mvCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Rocket. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
29. NEET Exam-style Question: If external torque is zero, conserved quantity is: A L B force C power D pressure
tau = r x FCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Conservation L. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
30. NEET Exam-style Question: Fastest among ring, disc, solid sphere on incline is:
v = R omegaCorrect Answer: Solid sphere because I/MR² is smallest.
Detailed Explanation: This is a rotation revision problem from Rolling race. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
31. NEET Exam-style Question: Two equal masses are at x=0 and x=8 m. COM is: A 0 B 4 C 8 D 16
COMCorrect Answer: B. Equal masses give midpoint.
Detailed Explanation: This is a rotation revision problem from COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
32. NEET Exam-style Question: Momentum of 2 kg body moving at 5 m/s is: A 5 B 7 C 10 D 20
p=mvCorrect Answer: C. p=mv=10 kg m/s.
Detailed Explanation: This is a rotation revision problem from Momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
33. NEET Exam-style Question: Torque is maximum when angle between r and F is: A 0 B 45 C 90 D 180
tau = r x FCorrect Answer: C. tau=rF sin theta.
Detailed Explanation: This is a rotation revision problem from Torque. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
34. NEET Exam-style Question: For rigid body L equals: A Iomega B mr C Fd D P/t
tau = r x FCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Angular momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
35. NEET Exam-style Question: Moment of inertia of ring about central axis is: A MR² B MR²/2 C MR²/4 D 2MR²/5
I = Sigma mr²Correct Answer: A.
Detailed Explanation: This is a rotation revision problem from MOI. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
36. NEET Exam-style Question: Pure rolling condition is: A v=Romega B v=omega/R C a=omegaR D I=MR
v = R omegaCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Rolling. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
37. NEET Exam-style Question: Impulse equals: A Delta p B power C torque D energy
p=mvCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Impulse. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
38. NEET Exam-style Question: Rocket equation contains: A ln(M0/M) B sin theta C kx D MR²/2
p=mvCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Rocket. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
39. NEET Exam-style Question: If external torque is zero, conserved quantity is: A L B force C power D pressure
tau = r x FCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Conservation L. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
40. NEET Exam-style Question: Fastest among ring, disc, solid sphere on incline is:
v = R omegaCorrect Answer: Solid sphere because I/MR² is smallest.
Detailed Explanation: This is a rotation revision problem from Rolling race. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
41. NEET Exam-style Question: Two equal masses are at x=0 and x=8 m. COM is: A 0 B 4 C 8 D 16
COMCorrect Answer: B. Equal masses give midpoint.
Detailed Explanation: This is a rotation revision problem from COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
42. NEET Exam-style Question: Momentum of 2 kg body moving at 5 m/s is: A 5 B 7 C 10 D 20
p=mvCorrect Answer: C. p=mv=10 kg m/s.
Detailed Explanation: This is a rotation revision problem from Momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
43. NEET Exam-style Question: Torque is maximum when angle between r and F is: A 0 B 45 C 90 D 180
tau = r x FCorrect Answer: C. tau=rF sin theta.
Detailed Explanation: This is a rotation revision problem from Torque. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
44. NEET Exam-style Question: For rigid body L equals: A Iomega B mr C Fd D P/t
tau = r x FCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Angular momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
45. NEET Exam-style Question: Moment of inertia of ring about central axis is: A MR² B MR²/2 C MR²/4 D 2MR²/5
I = Sigma mr²Correct Answer: A.
Detailed Explanation: This is a rotation revision problem from MOI. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
46. NEET Exam-style Question: Pure rolling condition is: A v=Romega B v=omega/R C a=omegaR D I=MR
v = R omegaCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Rolling. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
47. NEET Exam-style Question: Impulse equals: A Delta p B power C torque D energy
p=mvCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Impulse. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
48. NEET Exam-style Question: Rocket equation contains: A ln(M0/M) B sin theta C kx D MR²/2
p=mvCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Rocket. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
49. NEET Exam-style Question: If external torque is zero, conserved quantity is: A L B force C power D pressure
tau = r x FCorrect Answer: A.
Detailed Explanation: This is a rotation revision problem from Conservation L. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
50. NEET Exam-style Question: Fastest among ring, disc, solid sphere on incline is:
v = R omegaCorrect Answer: Solid sphere because I/MR² is smallest.
Detailed Explanation: This is a rotation revision problem from Rolling race. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
12

JEE Main PYQs

1. JEE Main Exam-style Question: Masses 1,2,3 kg at x=0,2,4 m. Find xcm.
COMCorrect Answer: xcm=(0+4+12)/6=8/3 m.
Detailed Explanation: This is a rotation revision problem from COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
2. JEE Main Exam-style Question: Bullet 0.02 kg at 300 m/s leaves 2 kg gun. Recoil speed?
p=mvCorrect Answer: V=3 m/s opposite bullet.
Detailed Explanation: This is a rotation revision problem from Recoil. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
3. JEE Main Exam-style Question: r=3 m, F=20 N at 30 degrees. Find torque.
tau = r x FCorrect Answer: tau=30 N m.
Detailed Explanation: This is a rotation revision problem from Torque. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
4. JEE Main Exam-style Question: I=4, omega=5. Find L.
tau = r x FCorrect Answer: L=20 kg m²/s.
Detailed Explanation: This is a rotation revision problem from Angular momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
5. JEE Main Exam-style Question: Disc central I=MR²/2. Tangent parallel axis I?
I = Sigma mr²Correct Answer: 3MR²/2.
Detailed Explanation: This is a rotation revision problem from MOI axis. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
6. JEE Main Exam-style Question: Solid cylinder rolling KE at speed v.
v = R omegaCorrect Answer: 3/4 Mv².
Detailed Explanation: This is a rotation revision problem from Rolling energy. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
7. JEE Main Exam-style Question: u=2 km/s, M0/M=e. Speed gain?
p=mvCorrect Answer: 2 km/s.
Detailed Explanation: This is a rotation revision problem from Rocket. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
8. JEE Main Exam-style Question: Rod centre to end theorem result.
I = Sigma mr²Correct Answer: ML²/3.
Detailed Explanation: This is a rotation revision problem from Parallel axis. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
9. JEE Main Exam-style Question: Ring acceleration down incline.
v = R omegaCorrect Answer: g sin theta / 2.
Detailed Explanation: This is a rotation revision problem from Rolling incline. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
10. JEE Main Exam-style Question: Torque 6 N m for 5 s changes L by:
tau = r x FCorrect Answer: 30 kg m²/s.
Detailed Explanation: This is a rotation revision problem from Angular impulse. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
11. JEE Main Exam-style Question: Masses 1,2,3 kg at x=0,2,4 m. Find xcm.
COMCorrect Answer: xcm=(0+4+12)/6=8/3 m.
Detailed Explanation: This is a rotation revision problem from COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
12. JEE Main Exam-style Question: Bullet 0.02 kg at 300 m/s leaves 2 kg gun. Recoil speed?
p=mvCorrect Answer: V=3 m/s opposite bullet.
Detailed Explanation: This is a rotation revision problem from Recoil. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
13. JEE Main Exam-style Question: r=3 m, F=20 N at 30 degrees. Find torque.
tau = r x FCorrect Answer: tau=30 N m.
Detailed Explanation: This is a rotation revision problem from Torque. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
14. JEE Main Exam-style Question: I=4, omega=5. Find L.
tau = r x FCorrect Answer: L=20 kg m²/s.
Detailed Explanation: This is a rotation revision problem from Angular momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
15. JEE Main Exam-style Question: Disc central I=MR²/2. Tangent parallel axis I?
I = Sigma mr²Correct Answer: 3MR²/2.
Detailed Explanation: This is a rotation revision problem from MOI axis. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
16. JEE Main Exam-style Question: Solid cylinder rolling KE at speed v.
v = R omegaCorrect Answer: 3/4 Mv².
Detailed Explanation: This is a rotation revision problem from Rolling energy. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
17. JEE Main Exam-style Question: u=2 km/s, M0/M=e. Speed gain?
p=mvCorrect Answer: 2 km/s.
Detailed Explanation: This is a rotation revision problem from Rocket. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
18. JEE Main Exam-style Question: Rod centre to end theorem result.
I = Sigma mr²Correct Answer: ML²/3.
Detailed Explanation: This is a rotation revision problem from Parallel axis. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
19. JEE Main Exam-style Question: Ring acceleration down incline.
v = R omegaCorrect Answer: g sin theta / 2.
Detailed Explanation: This is a rotation revision problem from Rolling incline. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
20. JEE Main Exam-style Question: Torque 6 N m for 5 s changes L by:
tau = r x FCorrect Answer: 30 kg m²/s.
Detailed Explanation: This is a rotation revision problem from Angular impulse. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
21. JEE Main Exam-style Question: Masses 1,2,3 kg at x=0,2,4 m. Find xcm.
COMCorrect Answer: xcm=(0+4+12)/6=8/3 m.
Detailed Explanation: This is a rotation revision problem from COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
22. JEE Main Exam-style Question: Bullet 0.02 kg at 300 m/s leaves 2 kg gun. Recoil speed?
p=mvCorrect Answer: V=3 m/s opposite bullet.
Detailed Explanation: This is a rotation revision problem from Recoil. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
23. JEE Main Exam-style Question: r=3 m, F=20 N at 30 degrees. Find torque.
tau = r x FCorrect Answer: tau=30 N m.
Detailed Explanation: This is a rotation revision problem from Torque. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
24. JEE Main Exam-style Question: I=4, omega=5. Find L.
tau = r x FCorrect Answer: L=20 kg m²/s.
Detailed Explanation: This is a rotation revision problem from Angular momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
25. JEE Main Exam-style Question: Disc central I=MR²/2. Tangent parallel axis I?
I = Sigma mr²Correct Answer: 3MR²/2.
Detailed Explanation: This is a rotation revision problem from MOI axis. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
26. JEE Main Exam-style Question: Solid cylinder rolling KE at speed v.
v = R omegaCorrect Answer: 3/4 Mv².
Detailed Explanation: This is a rotation revision problem from Rolling energy. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
27. JEE Main Exam-style Question: u=2 km/s, M0/M=e. Speed gain?
p=mvCorrect Answer: 2 km/s.
Detailed Explanation: This is a rotation revision problem from Rocket. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
28. JEE Main Exam-style Question: Rod centre to end theorem result.
I = Sigma mr²Correct Answer: ML²/3.
Detailed Explanation: This is a rotation revision problem from Parallel axis. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
29. JEE Main Exam-style Question: Ring acceleration down incline.
v = R omegaCorrect Answer: g sin theta / 2.
Detailed Explanation: This is a rotation revision problem from Rolling incline. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
30. JEE Main Exam-style Question: Torque 6 N m for 5 s changes L by:
tau = r x FCorrect Answer: 30 kg m²/s.
Detailed Explanation: This is a rotation revision problem from Angular impulse. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
31. JEE Main Exam-style Question: Masses 1,2,3 kg at x=0,2,4 m. Find xcm.
COMCorrect Answer: xcm=(0+4+12)/6=8/3 m.
Detailed Explanation: This is a rotation revision problem from COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
32. JEE Main Exam-style Question: Bullet 0.02 kg at 300 m/s leaves 2 kg gun. Recoil speed?
p=mvCorrect Answer: V=3 m/s opposite bullet.
Detailed Explanation: This is a rotation revision problem from Recoil. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
33. JEE Main Exam-style Question: r=3 m, F=20 N at 30 degrees. Find torque.
tau = r x FCorrect Answer: tau=30 N m.
Detailed Explanation: This is a rotation revision problem from Torque. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
34. JEE Main Exam-style Question: I=4, omega=5. Find L.
tau = r x FCorrect Answer: L=20 kg m²/s.
Detailed Explanation: This is a rotation revision problem from Angular momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
35. JEE Main Exam-style Question: Disc central I=MR²/2. Tangent parallel axis I?
I = Sigma mr²Correct Answer: 3MR²/2.
Detailed Explanation: This is a rotation revision problem from MOI axis. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
36. JEE Main Exam-style Question: Solid cylinder rolling KE at speed v.
v = R omegaCorrect Answer: 3/4 Mv².
Detailed Explanation: This is a rotation revision problem from Rolling energy. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
37. JEE Main Exam-style Question: u=2 km/s, M0/M=e. Speed gain?
p=mvCorrect Answer: 2 km/s.
Detailed Explanation: This is a rotation revision problem from Rocket. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
38. JEE Main Exam-style Question: Rod centre to end theorem result.
I = Sigma mr²Correct Answer: ML²/3.
Detailed Explanation: This is a rotation revision problem from Parallel axis. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
39. JEE Main Exam-style Question: Ring acceleration down incline.
v = R omegaCorrect Answer: g sin theta / 2.
Detailed Explanation: This is a rotation revision problem from Rolling incline. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
40. JEE Main Exam-style Question: Torque 6 N m for 5 s changes L by:
tau = r x FCorrect Answer: 30 kg m²/s.
Detailed Explanation: This is a rotation revision problem from Angular impulse. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
41. JEE Main Exam-style Question: Masses 1,2,3 kg at x=0,2,4 m. Find xcm.
COMCorrect Answer: xcm=(0+4+12)/6=8/3 m.
Detailed Explanation: This is a rotation revision problem from COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
42. JEE Main Exam-style Question: Bullet 0.02 kg at 300 m/s leaves 2 kg gun. Recoil speed?
p=mvCorrect Answer: V=3 m/s opposite bullet.
Detailed Explanation: This is a rotation revision problem from Recoil. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
43. JEE Main Exam-style Question: r=3 m, F=20 N at 30 degrees. Find torque.
tau = r x FCorrect Answer: tau=30 N m.
Detailed Explanation: This is a rotation revision problem from Torque. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
44. JEE Main Exam-style Question: I=4, omega=5. Find L.
tau = r x FCorrect Answer: L=20 kg m²/s.
Detailed Explanation: This is a rotation revision problem from Angular momentum. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
45. JEE Main Exam-style Question: Disc central I=MR²/2. Tangent parallel axis I?
I = Sigma mr²Correct Answer: 3MR²/2.
Detailed Explanation: This is a rotation revision problem from MOI axis. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
46. JEE Main Exam-style Question: Solid cylinder rolling KE at speed v.
v = R omegaCorrect Answer: 3/4 Mv².
Detailed Explanation: This is a rotation revision problem from Rolling energy. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
47. JEE Main Exam-style Question: u=2 km/s, M0/M=e. Speed gain?
p=mvCorrect Answer: 2 km/s.
Detailed Explanation: This is a rotation revision problem from Rocket. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
48. JEE Main Exam-style Question: Rod centre to end theorem result.
I = Sigma mr²Correct Answer: ML²/3.
Detailed Explanation: This is a rotation revision problem from Parallel axis. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
49. JEE Main Exam-style Question: Ring acceleration down incline.
v = R omegaCorrect Answer: g sin theta / 2.
Detailed Explanation: This is a rotation revision problem from Rolling incline. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
50. JEE Main Exam-style Question: Torque 6 N m for 5 s changes L by:
tau = r x FCorrect Answer: 30 kg m²/s.
Detailed Explanation: This is a rotation revision problem from Angular impulse. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
13

JEE Advanced PYQs

Advanced practice on COM, torque, angular momentum, MOI, rolling and composite systems.

1. JEE Advanced Exam-style Question: Square plate with corner removed: what method?
COMCorrect Answer: Treat removed part as negative mass with same origin.
Detailed Explanation: This is a rotation revision problem from Composite COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
2. JEE Advanced Exam-style Question: Derive ideal rocket velocity gain.
p=mvCorrect Answer: dv=-u dM/M, so Delta v=u ln(M0/M).
Detailed Explanation: This is a rotation revision problem from Rocket motion. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
3. JEE Advanced Exam-style Question: r=(2i+3j), F=(4i+5j). Find tau_z.
tau = r x FCorrect Answer: 2*5-3*4=-2 N m.
Detailed Explanation: This is a rotation revision problem from r x F. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
4. JEE Advanced Exam-style Question: If I halves with L conserved, omega becomes?
tau = r x FCorrect Answer: Doubles.
Detailed Explanation: This is a rotation revision problem from Variable I. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
5. JEE Advanced Exam-style Question: Rod centre MOI by integration.
I = Sigma mr²Correct Answer: Integral x²(M/L)dx from -L/2 to L/2 = ML²/12.
Detailed Explanation: This is a rotation revision problem from MOI integration. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
6. JEE Advanced Exam-style Question: Differentiate v=Romega.
v = R omegaCorrect Answer: a=Ralpha.
Detailed Explanation: This is a rotation revision problem from Rolling constraint. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
7. JEE Advanced Exam-style Question: String not slipping on pulley gives relation:
v = R omegaCorrect Answer: a=Ralpha.
Detailed Explanation: This is a rotation revision problem from Pulley inertia. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
8. JEE Advanced Exam-style Question: Disc with concentric hole MOI method.
I = Sigma mr²Correct Answer: Subtract removed disc MOI from full disc about same axis.
Detailed Explanation: This is a rotation revision problem from Cut-out MOI. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
9. JEE Advanced Exam-style Question: Projectile explodes in air; COM path?
COMCorrect Answer: Original projectile path under external gravity.
Detailed Explanation: This is a rotation revision problem from Projectile COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
10. JEE Advanced Exam-style Question: Area under tau-theta graph gives:
v = R omegaCorrect Answer: Rotational work.
Detailed Explanation: This is a rotation revision problem from Rolling graph. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
11. JEE Advanced Exam-style Question: Square plate with corner removed: what method?
COMCorrect Answer: Treat removed part as negative mass with same origin.
Detailed Explanation: This is a rotation revision problem from Composite COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
12. JEE Advanced Exam-style Question: Derive ideal rocket velocity gain.
p=mvCorrect Answer: dv=-u dM/M, so Delta v=u ln(M0/M).
Detailed Explanation: This is a rotation revision problem from Rocket motion. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
13. JEE Advanced Exam-style Question: r=(2i+3j), F=(4i+5j). Find tau_z.
tau = r x FCorrect Answer: 2*5-3*4=-2 N m.
Detailed Explanation: This is a rotation revision problem from r x F. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
14. JEE Advanced Exam-style Question: If I halves with L conserved, omega becomes?
tau = r x FCorrect Answer: Doubles.
Detailed Explanation: This is a rotation revision problem from Variable I. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
15. JEE Advanced Exam-style Question: Rod centre MOI by integration.
I = Sigma mr²Correct Answer: Integral x²(M/L)dx from -L/2 to L/2 = ML²/12.
Detailed Explanation: This is a rotation revision problem from MOI integration. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
16. JEE Advanced Exam-style Question: Differentiate v=Romega.
v = R omegaCorrect Answer: a=Ralpha.
Detailed Explanation: This is a rotation revision problem from Rolling constraint. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
17. JEE Advanced Exam-style Question: String not slipping on pulley gives relation:
v = R omegaCorrect Answer: a=Ralpha.
Detailed Explanation: This is a rotation revision problem from Pulley inertia. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
18. JEE Advanced Exam-style Question: Disc with concentric hole MOI method.
I = Sigma mr²Correct Answer: Subtract removed disc MOI from full disc about same axis.
Detailed Explanation: This is a rotation revision problem from Cut-out MOI. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
19. JEE Advanced Exam-style Question: Projectile explodes in air; COM path?
COMCorrect Answer: Original projectile path under external gravity.
Detailed Explanation: This is a rotation revision problem from Projectile COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
20. JEE Advanced Exam-style Question: Area under tau-theta graph gives:
v = R omegaCorrect Answer: Rotational work.
Detailed Explanation: This is a rotation revision problem from Rolling graph. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
21. JEE Advanced Exam-style Question: Square plate with corner removed: what method?
COMCorrect Answer: Treat removed part as negative mass with same origin.
Detailed Explanation: This is a rotation revision problem from Composite COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
22. JEE Advanced Exam-style Question: Derive ideal rocket velocity gain.
p=mvCorrect Answer: dv=-u dM/M, so Delta v=u ln(M0/M).
Detailed Explanation: This is a rotation revision problem from Rocket motion. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
23. JEE Advanced Exam-style Question: r=(2i+3j), F=(4i+5j). Find tau_z.
tau = r x FCorrect Answer: 2*5-3*4=-2 N m.
Detailed Explanation: This is a rotation revision problem from r x F. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
24. JEE Advanced Exam-style Question: If I halves with L conserved, omega becomes?
tau = r x FCorrect Answer: Doubles.
Detailed Explanation: This is a rotation revision problem from Variable I. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
25. JEE Advanced Exam-style Question: Rod centre MOI by integration.
I = Sigma mr²Correct Answer: Integral x²(M/L)dx from -L/2 to L/2 = ML²/12.
Detailed Explanation: This is a rotation revision problem from MOI integration. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
26. JEE Advanced Exam-style Question: Differentiate v=Romega.
v = R omegaCorrect Answer: a=Ralpha.
Detailed Explanation: This is a rotation revision problem from Rolling constraint. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
27. JEE Advanced Exam-style Question: String not slipping on pulley gives relation:
v = R omegaCorrect Answer: a=Ralpha.
Detailed Explanation: This is a rotation revision problem from Pulley inertia. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
28. JEE Advanced Exam-style Question: Disc with concentric hole MOI method.
I = Sigma mr²Correct Answer: Subtract removed disc MOI from full disc about same axis.
Detailed Explanation: This is a rotation revision problem from Cut-out MOI. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
29. JEE Advanced Exam-style Question: Projectile explodes in air; COM path?
COMCorrect Answer: Original projectile path under external gravity.
Detailed Explanation: This is a rotation revision problem from Projectile COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
30. JEE Advanced Exam-style Question: Area under tau-theta graph gives:
v = R omegaCorrect Answer: Rotational work.
Detailed Explanation: This is a rotation revision problem from Rolling graph. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
31. JEE Advanced Exam-style Question: Square plate with corner removed: what method?
COMCorrect Answer: Treat removed part as negative mass with same origin.
Detailed Explanation: This is a rotation revision problem from Composite COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
32. JEE Advanced Exam-style Question: Derive ideal rocket velocity gain.
p=mvCorrect Answer: dv=-u dM/M, so Delta v=u ln(M0/M).
Detailed Explanation: This is a rotation revision problem from Rocket motion. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
33. JEE Advanced Exam-style Question: r=(2i+3j), F=(4i+5j). Find tau_z.
tau = r x FCorrect Answer: 2*5-3*4=-2 N m.
Detailed Explanation: This is a rotation revision problem from r x F. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
34. JEE Advanced Exam-style Question: If I halves with L conserved, omega becomes?
tau = r x FCorrect Answer: Doubles.
Detailed Explanation: This is a rotation revision problem from Variable I. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
35. JEE Advanced Exam-style Question: Rod centre MOI by integration.
I = Sigma mr²Correct Answer: Integral x²(M/L)dx from -L/2 to L/2 = ML²/12.
Detailed Explanation: This is a rotation revision problem from MOI integration. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
36. JEE Advanced Exam-style Question: Differentiate v=Romega.
v = R omegaCorrect Answer: a=Ralpha.
Detailed Explanation: This is a rotation revision problem from Rolling constraint. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
37. JEE Advanced Exam-style Question: String not slipping on pulley gives relation:
v = R omegaCorrect Answer: a=Ralpha.
Detailed Explanation: This is a rotation revision problem from Pulley inertia. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
38. JEE Advanced Exam-style Question: Disc with concentric hole MOI method.
I = Sigma mr²Correct Answer: Subtract removed disc MOI from full disc about same axis.
Detailed Explanation: This is a rotation revision problem from Cut-out MOI. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
39. JEE Advanced Exam-style Question: Projectile explodes in air; COM path?
COMCorrect Answer: Original projectile path under external gravity.
Detailed Explanation: This is a rotation revision problem from Projectile COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
40. JEE Advanced Exam-style Question: Area under tau-theta graph gives:
v = R omegaCorrect Answer: Rotational work.
Detailed Explanation: This is a rotation revision problem from Rolling graph. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
41. JEE Advanced Exam-style Question: Square plate with corner removed: what method?
COMCorrect Answer: Treat removed part as negative mass with same origin.
Detailed Explanation: This is a rotation revision problem from Composite COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
42. JEE Advanced Exam-style Question: Derive ideal rocket velocity gain.
p=mvCorrect Answer: dv=-u dM/M, so Delta v=u ln(M0/M).
Detailed Explanation: This is a rotation revision problem from Rocket motion. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
43. JEE Advanced Exam-style Question: r=(2i+3j), F=(4i+5j). Find tau_z.
tau = r x FCorrect Answer: 2*5-3*4=-2 N m.
Detailed Explanation: This is a rotation revision problem from r x F. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
44. JEE Advanced Exam-style Question: If I halves with L conserved, omega becomes?
tau = r x FCorrect Answer: Doubles.
Detailed Explanation: This is a rotation revision problem from Variable I. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
45. JEE Advanced Exam-style Question: Rod centre MOI by integration.
I = Sigma mr²Correct Answer: Integral x²(M/L)dx from -L/2 to L/2 = ML²/12.
Detailed Explanation: This is a rotation revision problem from MOI integration. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
46. JEE Advanced Exam-style Question: Differentiate v=Romega.
v = R omegaCorrect Answer: a=Ralpha.
Detailed Explanation: This is a rotation revision problem from Rolling constraint. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
47. JEE Advanced Exam-style Question: String not slipping on pulley gives relation:
v = R omegaCorrect Answer: a=Ralpha.
Detailed Explanation: This is a rotation revision problem from Pulley inertia. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
48. JEE Advanced Exam-style Question: Disc with concentric hole MOI method.
I = Sigma mr²Correct Answer: Subtract removed disc MOI from full disc about same axis.
Detailed Explanation: This is a rotation revision problem from Cut-out MOI. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
49. JEE Advanced Exam-style Question: Projectile explodes in air; COM path?
COMCorrect Answer: Original projectile path under external gravity.
Detailed Explanation: This is a rotation revision problem from Projectile COM. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.
50. JEE Advanced Exam-style Question: Area under tau-theta graph gives:
v = R omegaCorrect Answer: Rotational work.
Detailed Explanation: This is a rotation revision problem from Rolling graph. Select the correct chapter formula first, keep vector signs where needed, and use axis/rolling constraints only under their valid conditions.

Searching for a Physics Tutor? If Centre of Mass, Momentum, Torque, Angular Momentum, Moment of Inertia or Rolling Motion is not clear, contact Kumar Sir.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar SirVisit WebsiteEmail Kumar Sir
14

IB Questions

IB 1. Define centre of mass.
Weighted average position of mass.
IB 2. State impulse-momentum theorem.
Impulse equals change in momentum.
IB 3. State torque formula.
tau=r x F.
IB 4. Angular momentum of rigid body.
L=Iomega.
IB 5. Conservation of angular momentum condition.
Net external torque zero.
IB 6. Moment of inertia definition.
I=sum mr² or integral r²dm.
IB 7. Radius of gyration formula.
I=Mk².
IB 8. Parallel axis theorem.
I=Icm+Md².
IB 9. Perpendicular axis theorem.
Iz=Ix+Iy for plane lamina.
IB 10. Pure rolling condition.
v=Romega.
IB 11. Total rolling KE.
1/2Mv²+1/2Iomega².
IB 12. Rocket equation.
v=u ln(M0/M).
IB 13. Recoil principle.
Momentum conservation.
IB 14. Torque-power relation.
P=tau omega.
IB 15. Work in rotation.
W=tau theta.
IB 16. Disc central MOI.
MR²/2.
IB 17. Ring central MOI.
MR².
IB 18. Solid sphere MOI.
2MR²/5.
IB 19. Hollow sphere MOI.
2MR²/3.
IB 20. Rolling incline acceleration.
g sin theta/(1+I/MR²).
IB 21. Angular velocity unit.
rad/s.
IB 22. Torque unit.
N m.
IB 23. Momentum unit.
kg m/s.
IB 24. Angular momentum unit.
kg m²/s.
IB 25. Most important rolling trap.
Do not use v=Romega during slipping.
15

IGCSE Questions

IGCSE 1. Define centre of mass.
Weighted average position of mass.
IGCSE 2. State impulse-momentum theorem.
Impulse equals change in momentum.
IGCSE 3. State torque formula.
tau=r x F.
IGCSE 4. Angular momentum of rigid body.
L=Iomega.
IGCSE 5. Conservation of angular momentum condition.
Net external torque zero.
IGCSE 6. Moment of inertia definition.
I=sum mr² or integral r²dm.
IGCSE 7. Radius of gyration formula.
I=Mk².
IGCSE 8. Parallel axis theorem.
I=Icm+Md².
IGCSE 9. Perpendicular axis theorem.
Iz=Ix+Iy for plane lamina.
IGCSE 10. Pure rolling condition.
v=Romega.
IGCSE 11. Total rolling KE.
1/2Mv²+1/2Iomega².
IGCSE 12. Rocket equation.
v=u ln(M0/M).
IGCSE 13. Recoil principle.
Momentum conservation.
IGCSE 14. Torque-power relation.
P=tau omega.
IGCSE 15. Work in rotation.
W=tau theta.
IGCSE 16. Disc central MOI.
MR²/2.
IGCSE 17. Ring central MOI.
MR².
IGCSE 18. Solid sphere MOI.
2MR²/5.
IGCSE 19. Hollow sphere MOI.
2MR²/3.
IGCSE 20. Rolling incline acceleration.
g sin theta/(1+I/MR²).
IGCSE 21. Angular velocity unit.
rad/s.
IGCSE 22. Torque unit.
N m.
IGCSE 23. Momentum unit.
kg m/s.
IGCSE 24. Angular momentum unit.
kg m²/s.
IGCSE 25. Most important rolling trap.
Do not use v=Romega during slipping.
16

A-Level Questions

A-Level 1. Define centre of mass.
Weighted average position of mass.
A-Level 2. State impulse-momentum theorem.
Impulse equals change in momentum.
A-Level 3. State torque formula.
tau=r x F.
A-Level 4. Angular momentum of rigid body.
L=Iomega.
A-Level 5. Conservation of angular momentum condition.
Net external torque zero.
A-Level 6. Moment of inertia definition.
I=sum mr² or integral r²dm.
A-Level 7. Radius of gyration formula.
I=Mk².
A-Level 8. Parallel axis theorem.
I=Icm+Md².
A-Level 9. Perpendicular axis theorem.
Iz=Ix+Iy for plane lamina.
A-Level 10. Pure rolling condition.
v=Romega.
A-Level 11. Total rolling KE.
1/2Mv²+1/2Iomega².
A-Level 12. Rocket equation.
v=u ln(M0/M).
A-Level 13. Recoil principle.
Momentum conservation.
A-Level 14. Torque-power relation.
P=tau omega.
A-Level 15. Work in rotation.
W=tau theta.
A-Level 16. Disc central MOI.
MR²/2.
A-Level 17. Ring central MOI.
MR².
A-Level 18. Solid sphere MOI.
2MR²/5.
A-Level 19. Hollow sphere MOI.
2MR²/3.
A-Level 20. Rolling incline acceleration.
g sin theta/(1+I/MR²).
A-Level 21. Angular velocity unit.
rad/s.
A-Level 22. Torque unit.
N m.
A-Level 23. Momentum unit.
kg m/s.
A-Level 24. Angular momentum unit.
kg m²/s.
A-Level 25. Most important rolling trap.
Do not use v=Romega during slipping.
17

Assertion Reason

1. Assertion: COM can lie outside the body. Reason: Ring COM lies at its centre.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
2. Assertion: Momentum is conserved if external impulse is zero. Reason: Internal forces cancel.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
3. Assertion: Torque is force only. Reason: Moment arm affects turning effect.
Answer: Assertion false, reason true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
4. Assertion: Angular momentum is conserved when external torque is zero. Reason: tau=dL/dt.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
5. Assertion: Ring has greater MOI than disc for same M,R. Reason: Mass is farther from axis.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
6. Assertion: Pure rolling means v=Romega. Reason: Contact point is instantaneously at rest.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
7. Assertion: Perpendicular axis theorem applies to all solids. Reason: Iz=Ix+Iy.
Answer: Assertion false; theorem is for plane lamina.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
8. Assertion: Rocket can move in vacuum. Reason: It ejects mass backward.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
9. Assertion: Rolling KE is only translational KE. Reason: Rolling body also rotates.
Answer: Assertion false, reason true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
10. Assertion: Parallel axis theorem adds Md². Reason: Shifted axis is parallel to COM axis.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
11. Assertion: COM can lie outside the body. Reason: Ring COM lies at its centre.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
12. Assertion: Momentum is conserved if external impulse is zero. Reason: Internal forces cancel.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
13. Assertion: Torque is force only. Reason: Moment arm affects turning effect.
Answer: Assertion false, reason true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
14. Assertion: Angular momentum is conserved when external torque is zero. Reason: tau=dL/dt.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
15. Assertion: Ring has greater MOI than disc for same M,R. Reason: Mass is farther from axis.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
16. Assertion: Pure rolling means v=Romega. Reason: Contact point is instantaneously at rest.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
17. Assertion: Perpendicular axis theorem applies to all solids. Reason: Iz=Ix+Iy.
Answer: Assertion false; theorem is for plane lamina.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
18. Assertion: Rocket can move in vacuum. Reason: It ejects mass backward.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
19. Assertion: Rolling KE is only translational KE. Reason: Rolling body also rotates.
Answer: Assertion false, reason true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
20. Assertion: Parallel axis theorem adds Md². Reason: Shifted axis is parallel to COM axis.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
21. Assertion: COM can lie outside the body. Reason: Ring COM lies at its centre.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
22. Assertion: Momentum is conserved if external impulse is zero. Reason: Internal forces cancel.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
23. Assertion: Torque is force only. Reason: Moment arm affects turning effect.
Answer: Assertion false, reason true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
24. Assertion: Angular momentum is conserved when external torque is zero. Reason: tau=dL/dt.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
25. Assertion: Ring has greater MOI than disc for same M,R. Reason: Mass is farther from axis.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
26. Assertion: Pure rolling means v=Romega. Reason: Contact point is instantaneously at rest.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
27. Assertion: Perpendicular axis theorem applies to all solids. Reason: Iz=Ix+Iy.
Answer: Assertion false; theorem is for plane lamina.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
28. Assertion: Rocket can move in vacuum. Reason: It ejects mass backward.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
29. Assertion: Rolling KE is only translational KE. Reason: Rolling body also rotates.
Answer: Assertion false, reason true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
30. Assertion: Parallel axis theorem adds Md². Reason: Shifted axis is parallel to COM axis.
Answer: Both true.
Explanation: Check the validity condition: isolated system, zero torque, same axis, pure rolling or plane lamina.
18

Case Study Questions

Case Study: COM of composite bodies
COMPassage: Use component masses and coordinates; removed parts are negative mass.
Answers and Explanations: Apply the listed formula, check the condition, and keep signs/axis consistent.
Case Study: Rocket motion
p=mvPassage: Variable mass system; v=u ln(M0/M).
Answers and Explanations: Apply the listed formula, check the condition, and keep signs/axis consistent.
Case Study: Recoil
p=mvPassage: Bullet and gun momenta are equal and opposite.
Answers and Explanations: Apply the listed formula, check the condition, and keep signs/axis consistent.
Case Study: Torque applications
tau = r x FPassage: Door/wrench torque depends on perpendicular distance.
Answers and Explanations: Apply the listed formula, check the condition, and keep signs/axis consistent.
Case Study: Rotating stool
tau = r x FPassage: I decreases, omega increases if L is conserved.
Answers and Explanations: Apply the listed formula, check the condition, and keep signs/axis consistent.
Case Study: Rolling cylinder
v = R omegaPassage: K=3/4Mv² and a=2g sin theta/3.
Answers and Explanations: Apply the listed formula, check the condition, and keep signs/axis consistent.
Case Study: Rolling sphere
v = R omegaPassage: Solid sphere has a=5g sin theta/7 and reaches before ring.
Answers and Explanations: Apply the listed formula, check the condition, and keep signs/axis consistent.
19

Quick Revision Notes

Most Important Formulas

  • xcm=Σmx/Σm
  • p=mv, J=Δp
  • τ=r×F
  • L=Iω
  • I=Σmr²
  • v=Rω

Most Important Derivations

  • COM weighted average
  • Rocket equation
  • τ=dL/dt
  • Parallel axis theorem
  • Rolling incline acceleration

NEET Traps

  • Wrong MOI formula
  • Forgetting vector direction
  • Using v=Rω during slipping
  • Confusing torque and work units

JEE Traps

  • Cut-out COM and MOI
  • External torque/impulse conditions
  • Composite systems
  • Pulley/spool constraints

Repeated PYQ Concepts

  • Rolling race
  • Skater pulling arms
  • Disc/ring/sphere MOI
  • Recoil and explosion
  • Torque moment arm

Searching for a Physics Tutor? If Centre of Mass, Momentum, Torque, Angular Momentum, Moment of Inertia or Rolling Motion is not clear, contact Kumar Sir.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar SirVisit WebsiteEmail Kumar Sir
Scroll to Top