Torque and Angular Momentum

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Class 11 Physics - Rotation

Torque and Angular Momentum

Master torque, moment of force, couple, angular momentum, conservation of angular momentum, applications, numericals and PYQs.

CBSENEETJEE MainJEE AdvancedIBIGCSEA-Level
01

Torque

Torque is the rotational effect of a force about a point or axis. It is a vector directed by the right-hand rule.

τ = r × F|τ| = rF sinθ
  • SI unit: N m.
  • Dimensions: ML2T-2.
  • Maximum when force is perpendicular to radius.
  • Zero if line of action passes through pivot.
moment arm
02

Moment of Force

Moment of force equals force times perpendicular distance from pivot to line of action.

τ = Fd

d is the moment arm. Clockwise moments and anticlockwise moments must be assigned signs consistently.

moment arm
03

Couple

A couple is two equal and opposite parallel forces. Net force is zero, but net torque is non-zero.

τ = F × perpendicular distance between forces

Steering wheel, screwdriver and bottle cap are classic couple examples.

net force 0, torque non-zero
04

Angular Momentum

Angular momentum is rotational momentum. It is a vector and direction is given by the right-hand rule.

L = r × p|L| = rp sinθL = Iω

Unit: kg m2/s. Dimension: ML2T-1.

rp
05

Relation Between Torque and Angular Momentum

Torque changes angular momentum. If torque is zero, angular momentum remains constant.

τ = dL/dt

Angular impulse equals change in angular momentum: ∫τdt = ΔL.

Ltslope = tau
06

Conservation of Angular Momentum

If net external torque on a system is zero, total angular momentum remains conserved.

I1ω1 = I2ω2
  • If I decreases, omega increases.
  • Direction of angular momentum is conserved too.
  • Skater, rotating chair and planetary motion use this idea.
I decreases, omega increases
07

Applications

Application cards with concept, formula, diagram and exam tip.

Opening a door

moment arm

Concept: Torque about hinge

Formula: tau=Fd

Exam Tip: Push far from hinge.

Wrench and nut

moment arm

Concept: Long handle increases moment arm

Formula: tau=Fd

Exam Tip: Perpendicular push is best.

Steering wheel

net force 0, torque non-zero

Concept: Two hands form couple

Formula: tau=F d

Exam Tip: Net force can be zero.

Ice skater

I decreases, omega increases

Concept: Angular momentum conservation

Formula: I1w1=I2w2

Exam Tip: Pulling arms in increases speed.

Rotating chair with dumbbells

I decreases, omega increases

Concept: Variable moment of inertia

Formula: Iomega=constant

Exam Tip: No external torque condition.

Diving athlete

I decreases, omega increases

Concept: Tuck reduces I

Formula: I1w1=I2w2

Exam Tip: Rotation speeds up.

Cat landing on feet

I decreases, omega increases

Concept: Body parts rotate with angular momentum constraints

Formula: L conserved approximately

Exam Tip: Internal motion changes orientation.

Planetary motion

rp

Concept: Central force torque zero

Formula: L conserved

Exam Tip: Planet is faster near Sun.

Gyroscope

Ltslope = tau

Concept: Large angular momentum resists direction change

Formula: tau=dL/dt

Exam Tip: Torque changes direction of L.

Helicopter rotor

moment arm

Concept: Rotor torque needs counter torque

Formula: tau=dL/dt

Exam Tip: Tail rotor balances rotation.

Bicycle wheel

rp

Concept: Spinning wheel has angular momentum

Formula: L=Iomega

Exam Tip: Direction by right-hand rule.

Cricket bat swing

moment arm

Concept: Hands apply torque to bat

Formula: tau=Ialpha

Exam Tip: Farther force from pivot gives more rotation.

08

Important Formula Table

Compact formula table for fast revision.

QuantityFormulaUnitDimensionExam Tip
Torqueτ=r×F, rF sinθN mML²T^-2Use perpendicular component
Moment armd=r sinθmLPerpendicular distance
Coupleτ=FdN mML²T^-2Net force zero
Particle LL=r×pkg m²/sML²T^-1Use vector cross product
Rigid body LL=Iωkg m²/sML²T^-1Fixed axis
Torque-Lτ=dL/dtN mML²T^-2Torque changes L
ConservationI1ω1=I2ω2--Only if external torque zero

Searching for a Physics Tutor? If Torque, Couple, Angular Momentum or NEET/JEE rotational numericals are not clear, contact Kumar Sir.

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09

High-Quality Numericals

Solved bank for CBSE, NEET, JEE Main, JEE Advanced, IB, IGCSE and A-Level.

1. CBSE moment: A 15 N force acts at 0.4 m from pivot. Find moment.
moment armQuestion: A 15 N force acts at 0.4 m from pivot. Find moment.
Diagram: shown above.
Given: Identify pivot, force, perpendicular distance, I, omega or angular momentum.
Formula: tau=rF sin theta=Fd, L=r p sin theta, L=Iomega, tau=dL/dt, and I1omega1=I2omega2 when external torque is zero.
Calculation: tau=Fd=6 N m.
Final Answer: tau=Fd=6 N m.
Exam Tip: Draw the line of action and moment arm first.
Common Mistake: Using full distance instead of perpendicular distance.
2. NEET torque: r=2 m, F=10 N at 30 degrees. Find torque.
moment armQuestion: r=2 m, F=10 N at 30 degrees. Find torque.
Diagram: shown above.
Given: Identify pivot, force, perpendicular distance, I, omega or angular momentum.
Formula: tau=rF sin theta=Fd, L=r p sin theta, L=Iomega, tau=dL/dt, and I1omega1=I2omega2 when external torque is zero.
Calculation: tau=rF sin30=10 N m.
Final Answer: tau=rF sin30=10 N m.
Exam Tip: Draw the line of action and moment arm first.
Common Mistake: Using full distance instead of perpendicular distance.
3. JEE Main couple: Forces 20 N separated by 0.3 m form a couple. Find moment.
net force 0, torque non-zeroQuestion: Forces 20 N separated by 0.3 m form a couple. Find moment.
Diagram: shown above.
Given: Identify pivot, force, perpendicular distance, I, omega or angular momentum.
Formula: tau=rF sin theta=Fd, L=r p sin theta, L=Iomega, tau=dL/dt, and I1omega1=I2omega2 when external torque is zero.
Calculation: tau=6 N m.
Final Answer: tau=6 N m.
Exam Tip: Draw the line of action and moment arm first.
Common Mistake: Using full distance instead of perpendicular distance.
4. JEE Advanced vector torque: r=(2i+4j), F=(3i+5j). Find tau_z.
moment armQuestion: r=(2i+4j), F=(3i+5j). Find tau_z.
Diagram: shown above.
Given: Identify pivot, force, perpendicular distance, I, omega or angular momentum.
Formula: tau=rF sin theta=Fd, L=r p sin theta, L=Iomega, tau=dL/dt, and I1omega1=I2omega2 when external torque is zero.
Calculation: tau_z=2x5-4x3=-2 N m.
Final Answer: tau_z=2x5-4x3=-2 N m.
Exam Tip: Draw the line of action and moment arm first.
Common Mistake: Using full distance instead of perpendicular distance.
5. IB angular momentum: I=4 kg m², omega=3 rad/s. Find L.
rpQuestion: I=4 kg m², omega=3 rad/s. Find L.
Diagram: shown above.
Given: Identify pivot, force, perpendicular distance, I, omega or angular momentum.
Formula: tau=rF sin theta=Fd, L=r p sin theta, L=Iomega, tau=dL/dt, and I1omega1=I2omega2 when external torque is zero.
Calculation: L=12 kg m²/s.
Final Answer: L=12 kg m²/s.
Exam Tip: Draw the line of action and moment arm first.
Common Mistake: Using full distance instead of perpendicular distance.
6. IGCSE door: Force 25 N at 0.8 m from hinge. Find moment.
moment armQuestion: Force 25 N at 0.8 m from hinge. Find moment.
Diagram: shown above.
Given: Identify pivot, force, perpendicular distance, I, omega or angular momentum.
Formula: tau=rF sin theta=Fd, L=r p sin theta, L=Iomega, tau=dL/dt, and I1omega1=I2omega2 when external torque is zero.
Calculation: 20 N m.
Final Answer: 20 N m.
Exam Tip: Draw the line of action and moment arm first.
Common Mistake: Using full distance instead of perpendicular distance.
7. A-Level conservation: I reduces from 8 to 2, omega initially 5. Find final omega.
I decreases, omega increasesQuestion: I reduces from 8 to 2, omega initially 5. Find final omega.
Diagram: shown above.
Given: Identify pivot, force, perpendicular distance, I, omega or angular momentum.
Formula: tau=rF sin theta=Fd, L=r p sin theta, L=Iomega, tau=dL/dt, and I1omega1=I2omega2 when external torque is zero.
Calculation: omega=20 rad/s.
Final Answer: omega=20 rad/s.
Exam Tip: Draw the line of action and moment arm first.
Common Mistake: Using full distance instead of perpendicular distance.
8. Angular impulse: Torque 7 N m acts for 4 s. Find change in L.
Ltslope = tauQuestion: Torque 7 N m acts for 4 s. Find change in L.
Diagram: shown above.
Given: Identify pivot, force, perpendicular distance, I, omega or angular momentum.
Formula: tau=rF sin theta=Fd, L=r p sin theta, L=Iomega, tau=dL/dt, and I1omega1=I2omega2 when external torque is zero.
Calculation: Delta L=28 kg m²/s.
Final Answer: Delta L=28 kg m²/s.
Exam Tip: Draw the line of action and moment arm first.
Common Mistake: Using full distance instead of perpendicular distance.
9. Particle L: r=5 m and p=3 kg m/s perpendicular. Find L.
rpQuestion: r=5 m and p=3 kg m/s perpendicular. Find L.
Diagram: shown above.
Given: Identify pivot, force, perpendicular distance, I, omega or angular momentum.
Formula: tau=rF sin theta=Fd, L=r p sin theta, L=Iomega, tau=dL/dt, and I1omega1=I2omega2 when external torque is zero.
Calculation: 15 kg m²/s.
Final Answer: 15 kg m²/s.
Exam Tip: Draw the line of action and moment arm first.
Common Mistake: Using full distance instead of perpendicular distance.
10. Torque-alpha: Torque 18 N m acts on I=6 kg m². Find alpha.
moment armQuestion: Torque 18 N m acts on I=6 kg m². Find alpha.
Diagram: shown above.
Given: Identify pivot, force, perpendicular distance, I, omega or angular momentum.
Formula: tau=rF sin theta=Fd, L=r p sin theta, L=Iomega, tau=dL/dt, and I1omega1=I2omega2 when external torque is zero.
Calculation: alpha=3 rad/s².
Final Answer: alpha=3 rad/s².
Exam Tip: Draw the line of action and moment arm first.
Common Mistake: Using full distance instead of perpendicular distance.
10

NEET Question Bank

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

1. NEET Exam-style Question: A force 10 N acts at perpendicular distance 2 m. Torque is: A 5 B 10 C 20 D 40 N m
moment armCorrect Answer: C. tau=Fd=20 N m.
Detailed Explanation: This tests torque. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
2. NEET Exam-style Question: Torque is maximum when angle between r and F is: A 0 B 30 C 90 D 180 degrees
moment armCorrect Answer: C. tau=rF sin theta.
Detailed Explanation: This tests moment arm. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
3. NEET Exam-style Question: SI unit of torque is: A N B N m C kg m/s D J/s
moment armCorrect Answer: B. Torque unit is N m.
Detailed Explanation: This tests unit. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
4. NEET Exam-style Question: A couple has net force: A zero B F C 2F D infinite
net force 0, torque non-zeroCorrect Answer: A. Equal and opposite forces cancel.
Detailed Explanation: This tests couple. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
5. NEET Exam-style Question: Angular momentum of rigid body is: A Iomega B Fr C ma D mv
rpCorrect Answer: A. L=Iomega.
Detailed Explanation: This tests angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
6. NEET Exam-style Question: If external torque is zero, conserved quantity is: A force B angular momentum C power D pressure
I decreases, omega increasesCorrect Answer: B.
Detailed Explanation: This tests conservation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
7. NEET Exam-style Question: Direction of torque is given by: A left hand B right hand rule C Snell law D Fleming left only
moment armCorrect Answer: B.
Detailed Explanation: This tests right hand rule. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
8. NEET Exam-style Question: Torque equals rate of change of: A linear velocity B angular momentum C mass D radius
Ltslope = tauCorrect Answer: B.
Detailed Explanation: This tests tau dLdt. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
9. NEET Exam-style Question: Skater pulls arms inward. Moment of inertia decreases, angular speed: A decreases B increases C zero D unchanged always
I decreases, omega increasesCorrect Answer: B.
Detailed Explanation: This tests skater. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
10. NEET Exam-style Question: For particle, L magnitude is: A rp sin theta B r/p C p/r D rF
rpCorrect Answer: A.
Detailed Explanation: This tests particle L. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
11. NEET Exam-style Question: A force 10 N acts at perpendicular distance 2 m. Torque is: A 5 B 10 C 20 D 40 N m
moment armCorrect Answer: C. tau=Fd=20 N m.
Detailed Explanation: This tests torque. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
12. NEET Exam-style Question: Torque is maximum when angle between r and F is: A 0 B 30 C 90 D 180 degrees
moment armCorrect Answer: C. tau=rF sin theta.
Detailed Explanation: This tests moment arm. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
13. NEET Exam-style Question: SI unit of torque is: A N B N m C kg m/s D J/s
moment armCorrect Answer: B. Torque unit is N m.
Detailed Explanation: This tests unit. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
14. NEET Exam-style Question: A couple has net force: A zero B F C 2F D infinite
net force 0, torque non-zeroCorrect Answer: A. Equal and opposite forces cancel.
Detailed Explanation: This tests couple. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
15. NEET Exam-style Question: Angular momentum of rigid body is: A Iomega B Fr C ma D mv
rpCorrect Answer: A. L=Iomega.
Detailed Explanation: This tests angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
16. NEET Exam-style Question: If external torque is zero, conserved quantity is: A force B angular momentum C power D pressure
I decreases, omega increasesCorrect Answer: B.
Detailed Explanation: This tests conservation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
17. NEET Exam-style Question: Direction of torque is given by: A left hand B right hand rule C Snell law D Fleming left only
moment armCorrect Answer: B.
Detailed Explanation: This tests right hand rule. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
18. NEET Exam-style Question: Torque equals rate of change of: A linear velocity B angular momentum C mass D radius
Ltslope = tauCorrect Answer: B.
Detailed Explanation: This tests tau dLdt. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
19. NEET Exam-style Question: Skater pulls arms inward. Moment of inertia decreases, angular speed: A decreases B increases C zero D unchanged always
I decreases, omega increasesCorrect Answer: B.
Detailed Explanation: This tests skater. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
20. NEET Exam-style Question: For particle, L magnitude is: A rp sin theta B r/p C p/r D rF
rpCorrect Answer: A.
Detailed Explanation: This tests particle L. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
21. NEET Exam-style Question: A force 10 N acts at perpendicular distance 2 m. Torque is: A 5 B 10 C 20 D 40 N m
moment armCorrect Answer: C. tau=Fd=20 N m.
Detailed Explanation: This tests torque. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
22. NEET Exam-style Question: Torque is maximum when angle between r and F is: A 0 B 30 C 90 D 180 degrees
moment armCorrect Answer: C. tau=rF sin theta.
Detailed Explanation: This tests moment arm. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
23. NEET Exam-style Question: SI unit of torque is: A N B N m C kg m/s D J/s
moment armCorrect Answer: B. Torque unit is N m.
Detailed Explanation: This tests unit. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
24. NEET Exam-style Question: A couple has net force: A zero B F C 2F D infinite
net force 0, torque non-zeroCorrect Answer: A. Equal and opposite forces cancel.
Detailed Explanation: This tests couple. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
25. NEET Exam-style Question: Angular momentum of rigid body is: A Iomega B Fr C ma D mv
rpCorrect Answer: A. L=Iomega.
Detailed Explanation: This tests angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
26. NEET Exam-style Question: If external torque is zero, conserved quantity is: A force B angular momentum C power D pressure
I decreases, omega increasesCorrect Answer: B.
Detailed Explanation: This tests conservation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
27. NEET Exam-style Question: Direction of torque is given by: A left hand B right hand rule C Snell law D Fleming left only
moment armCorrect Answer: B.
Detailed Explanation: This tests right hand rule. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
28. NEET Exam-style Question: Torque equals rate of change of: A linear velocity B angular momentum C mass D radius
Ltslope = tauCorrect Answer: B.
Detailed Explanation: This tests tau dLdt. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
29. NEET Exam-style Question: Skater pulls arms inward. Moment of inertia decreases, angular speed: A decreases B increases C zero D unchanged always
I decreases, omega increasesCorrect Answer: B.
Detailed Explanation: This tests skater. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
30. NEET Exam-style Question: For particle, L magnitude is: A rp sin theta B r/p C p/r D rF
rpCorrect Answer: A.
Detailed Explanation: This tests particle L. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
31. NEET Exam-style Question: A force 10 N acts at perpendicular distance 2 m. Torque is: A 5 B 10 C 20 D 40 N m
moment armCorrect Answer: C. tau=Fd=20 N m.
Detailed Explanation: This tests torque. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
32. NEET Exam-style Question: Torque is maximum when angle between r and F is: A 0 B 30 C 90 D 180 degrees
moment armCorrect Answer: C. tau=rF sin theta.
Detailed Explanation: This tests moment arm. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
33. NEET Exam-style Question: SI unit of torque is: A N B N m C kg m/s D J/s
moment armCorrect Answer: B. Torque unit is N m.
Detailed Explanation: This tests unit. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
34. NEET Exam-style Question: A couple has net force: A zero B F C 2F D infinite
net force 0, torque non-zeroCorrect Answer: A. Equal and opposite forces cancel.
Detailed Explanation: This tests couple. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
35. NEET Exam-style Question: Angular momentum of rigid body is: A Iomega B Fr C ma D mv
rpCorrect Answer: A. L=Iomega.
Detailed Explanation: This tests angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
36. NEET Exam-style Question: If external torque is zero, conserved quantity is: A force B angular momentum C power D pressure
I decreases, omega increasesCorrect Answer: B.
Detailed Explanation: This tests conservation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
37. NEET Exam-style Question: Direction of torque is given by: A left hand B right hand rule C Snell law D Fleming left only
moment armCorrect Answer: B.
Detailed Explanation: This tests right hand rule. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
38. NEET Exam-style Question: Torque equals rate of change of: A linear velocity B angular momentum C mass D radius
Ltslope = tauCorrect Answer: B.
Detailed Explanation: This tests tau dLdt. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
39. NEET Exam-style Question: Skater pulls arms inward. Moment of inertia decreases, angular speed: A decreases B increases C zero D unchanged always
I decreases, omega increasesCorrect Answer: B.
Detailed Explanation: This tests skater. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
40. NEET Exam-style Question: For particle, L magnitude is: A rp sin theta B r/p C p/r D rF
rpCorrect Answer: A.
Detailed Explanation: This tests particle L. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
41. NEET Exam-style Question: A force 10 N acts at perpendicular distance 2 m. Torque is: A 5 B 10 C 20 D 40 N m
moment armCorrect Answer: C. tau=Fd=20 N m.
Detailed Explanation: This tests torque. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
42. NEET Exam-style Question: Torque is maximum when angle between r and F is: A 0 B 30 C 90 D 180 degrees
moment armCorrect Answer: C. tau=rF sin theta.
Detailed Explanation: This tests moment arm. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
43. NEET Exam-style Question: SI unit of torque is: A N B N m C kg m/s D J/s
moment armCorrect Answer: B. Torque unit is N m.
Detailed Explanation: This tests unit. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
44. NEET Exam-style Question: A couple has net force: A zero B F C 2F D infinite
net force 0, torque non-zeroCorrect Answer: A. Equal and opposite forces cancel.
Detailed Explanation: This tests couple. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
45. NEET Exam-style Question: Angular momentum of rigid body is: A Iomega B Fr C ma D mv
rpCorrect Answer: A. L=Iomega.
Detailed Explanation: This tests angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
46. NEET Exam-style Question: If external torque is zero, conserved quantity is: A force B angular momentum C power D pressure
I decreases, omega increasesCorrect Answer: B.
Detailed Explanation: This tests conservation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
47. NEET Exam-style Question: Direction of torque is given by: A left hand B right hand rule C Snell law D Fleming left only
moment armCorrect Answer: B.
Detailed Explanation: This tests right hand rule. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
48. NEET Exam-style Question: Torque equals rate of change of: A linear velocity B angular momentum C mass D radius
Ltslope = tauCorrect Answer: B.
Detailed Explanation: This tests tau dLdt. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
49. NEET Exam-style Question: Skater pulls arms inward. Moment of inertia decreases, angular speed: A decreases B increases C zero D unchanged always
I decreases, omega increasesCorrect Answer: B.
Detailed Explanation: This tests skater. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
50. NEET Exam-style Question: For particle, L magnitude is: A rp sin theta B r/p C p/r D rF
rpCorrect Answer: A.
Detailed Explanation: This tests particle L. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
11

JEE Main Question Bank

50 difficult JEE Main-style questions on torque, couple, angular momentum, conservation and vector direction.

1. JEE Main Exam-style Question: r=3 m, F=20 N, angle=30 degrees. Find torque magnitude.
moment armCorrect Answer: tau=rF sin30=30 N m.
Detailed Explanation: This tests torque. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
2. JEE Main Exam-style Question: Force 50 N has moment arm 0.4 m. Find moment.
moment armCorrect Answer: tau=Fd=20 N m.
Detailed Explanation: This tests moment arm. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
3. JEE Main Exam-style Question: Two forces 10 N separated by 0.5 m form a couple. Couple moment?
net force 0, torque non-zeroCorrect Answer: tau=F d=5 N m.
Detailed Explanation: This tests couple. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
4. JEE Main Exam-style Question: I=2 kg m² and omega=6 rad/s. Find L.
rpCorrect Answer: L=Iomega=12 kg m²/s.
Detailed Explanation: This tests angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
5. JEE Main Exam-style Question: r=4 m, p=5 kg m/s perpendicular. Find L.
rpCorrect Answer: L=rp=20 kg m²/s.
Detailed Explanation: This tests particle angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
6. JEE Main Exam-style Question: I changes from 6 to 2 kg m², omega initial 4 rad/s. Find final omega.
I decreases, omega increasesCorrect Answer: I1w1=I2w2, w2=12 rad/s.
Detailed Explanation: This tests conservation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
7. JEE Main Exam-style Question: Constant torque 8 N m acts for 3 s. Change in angular momentum?
Ltslope = tauCorrect Answer: Delta L=tau t=24 kg m²/s.
Detailed Explanation: This tests torque and L. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
8. JEE Main Exam-style Question: r along +x and F along +y. Torque direction?
moment armCorrect Answer: +z by right hand rule.
Detailed Explanation: This tests vector direction. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
9. JEE Main Exam-style Question: Clockwise torque is often taken as:
moment armCorrect Answer: Negative if anticlockwise is positive.
Detailed Explanation: This tests clockwise moment. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
10. JEE Main Exam-style Question: Torque 12 N m acts on I=3 kg m². Angular acceleration?
moment armCorrect Answer: alpha=tau/I=4 rad/s².
Detailed Explanation: This tests rotational dynamics. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
11. JEE Main Exam-style Question: r=3 m, F=20 N, angle=30 degrees. Find torque magnitude.
moment armCorrect Answer: tau=rF sin30=30 N m.
Detailed Explanation: This tests torque. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
12. JEE Main Exam-style Question: Force 50 N has moment arm 0.4 m. Find moment.
moment armCorrect Answer: tau=Fd=20 N m.
Detailed Explanation: This tests moment arm. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
13. JEE Main Exam-style Question: Two forces 10 N separated by 0.5 m form a couple. Couple moment?
net force 0, torque non-zeroCorrect Answer: tau=F d=5 N m.
Detailed Explanation: This tests couple. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
14. JEE Main Exam-style Question: I=2 kg m² and omega=6 rad/s. Find L.
rpCorrect Answer: L=Iomega=12 kg m²/s.
Detailed Explanation: This tests angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
15. JEE Main Exam-style Question: r=4 m, p=5 kg m/s perpendicular. Find L.
rpCorrect Answer: L=rp=20 kg m²/s.
Detailed Explanation: This tests particle angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
16. JEE Main Exam-style Question: I changes from 6 to 2 kg m², omega initial 4 rad/s. Find final omega.
I decreases, omega increasesCorrect Answer: I1w1=I2w2, w2=12 rad/s.
Detailed Explanation: This tests conservation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
17. JEE Main Exam-style Question: Constant torque 8 N m acts for 3 s. Change in angular momentum?
Ltslope = tauCorrect Answer: Delta L=tau t=24 kg m²/s.
Detailed Explanation: This tests torque and L. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
18. JEE Main Exam-style Question: r along +x and F along +y. Torque direction?
moment armCorrect Answer: +z by right hand rule.
Detailed Explanation: This tests vector direction. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
19. JEE Main Exam-style Question: Clockwise torque is often taken as:
moment armCorrect Answer: Negative if anticlockwise is positive.
Detailed Explanation: This tests clockwise moment. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
20. JEE Main Exam-style Question: Torque 12 N m acts on I=3 kg m². Angular acceleration?
moment armCorrect Answer: alpha=tau/I=4 rad/s².
Detailed Explanation: This tests rotational dynamics. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
21. JEE Main Exam-style Question: r=3 m, F=20 N, angle=30 degrees. Find torque magnitude.
moment armCorrect Answer: tau=rF sin30=30 N m.
Detailed Explanation: This tests torque. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
22. JEE Main Exam-style Question: Force 50 N has moment arm 0.4 m. Find moment.
moment armCorrect Answer: tau=Fd=20 N m.
Detailed Explanation: This tests moment arm. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
23. JEE Main Exam-style Question: Two forces 10 N separated by 0.5 m form a couple. Couple moment?
net force 0, torque non-zeroCorrect Answer: tau=F d=5 N m.
Detailed Explanation: This tests couple. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
24. JEE Main Exam-style Question: I=2 kg m² and omega=6 rad/s. Find L.
rpCorrect Answer: L=Iomega=12 kg m²/s.
Detailed Explanation: This tests angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
25. JEE Main Exam-style Question: r=4 m, p=5 kg m/s perpendicular. Find L.
rpCorrect Answer: L=rp=20 kg m²/s.
Detailed Explanation: This tests particle angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
26. JEE Main Exam-style Question: I changes from 6 to 2 kg m², omega initial 4 rad/s. Find final omega.
I decreases, omega increasesCorrect Answer: I1w1=I2w2, w2=12 rad/s.
Detailed Explanation: This tests conservation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
27. JEE Main Exam-style Question: Constant torque 8 N m acts for 3 s. Change in angular momentum?
Ltslope = tauCorrect Answer: Delta L=tau t=24 kg m²/s.
Detailed Explanation: This tests torque and L. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
28. JEE Main Exam-style Question: r along +x and F along +y. Torque direction?
moment armCorrect Answer: +z by right hand rule.
Detailed Explanation: This tests vector direction. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
29. JEE Main Exam-style Question: Clockwise torque is often taken as:
moment armCorrect Answer: Negative if anticlockwise is positive.
Detailed Explanation: This tests clockwise moment. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
30. JEE Main Exam-style Question: Torque 12 N m acts on I=3 kg m². Angular acceleration?
moment armCorrect Answer: alpha=tau/I=4 rad/s².
Detailed Explanation: This tests rotational dynamics. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
31. JEE Main Exam-style Question: r=3 m, F=20 N, angle=30 degrees. Find torque magnitude.
moment armCorrect Answer: tau=rF sin30=30 N m.
Detailed Explanation: This tests torque. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
32. JEE Main Exam-style Question: Force 50 N has moment arm 0.4 m. Find moment.
moment armCorrect Answer: tau=Fd=20 N m.
Detailed Explanation: This tests moment arm. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
33. JEE Main Exam-style Question: Two forces 10 N separated by 0.5 m form a couple. Couple moment?
net force 0, torque non-zeroCorrect Answer: tau=F d=5 N m.
Detailed Explanation: This tests couple. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
34. JEE Main Exam-style Question: I=2 kg m² and omega=6 rad/s. Find L.
rpCorrect Answer: L=Iomega=12 kg m²/s.
Detailed Explanation: This tests angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
35. JEE Main Exam-style Question: r=4 m, p=5 kg m/s perpendicular. Find L.
rpCorrect Answer: L=rp=20 kg m²/s.
Detailed Explanation: This tests particle angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
36. JEE Main Exam-style Question: I changes from 6 to 2 kg m², omega initial 4 rad/s. Find final omega.
I decreases, omega increasesCorrect Answer: I1w1=I2w2, w2=12 rad/s.
Detailed Explanation: This tests conservation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
37. JEE Main Exam-style Question: Constant torque 8 N m acts for 3 s. Change in angular momentum?
Ltslope = tauCorrect Answer: Delta L=tau t=24 kg m²/s.
Detailed Explanation: This tests torque and L. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
38. JEE Main Exam-style Question: r along +x and F along +y. Torque direction?
moment armCorrect Answer: +z by right hand rule.
Detailed Explanation: This tests vector direction. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
39. JEE Main Exam-style Question: Clockwise torque is often taken as:
moment armCorrect Answer: Negative if anticlockwise is positive.
Detailed Explanation: This tests clockwise moment. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
40. JEE Main Exam-style Question: Torque 12 N m acts on I=3 kg m². Angular acceleration?
moment armCorrect Answer: alpha=tau/I=4 rad/s².
Detailed Explanation: This tests rotational dynamics. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
41. JEE Main Exam-style Question: r=3 m, F=20 N, angle=30 degrees. Find torque magnitude.
moment armCorrect Answer: tau=rF sin30=30 N m.
Detailed Explanation: This tests torque. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
42. JEE Main Exam-style Question: Force 50 N has moment arm 0.4 m. Find moment.
moment armCorrect Answer: tau=Fd=20 N m.
Detailed Explanation: This tests moment arm. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
43. JEE Main Exam-style Question: Two forces 10 N separated by 0.5 m form a couple. Couple moment?
net force 0, torque non-zeroCorrect Answer: tau=F d=5 N m.
Detailed Explanation: This tests couple. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
44. JEE Main Exam-style Question: I=2 kg m² and omega=6 rad/s. Find L.
rpCorrect Answer: L=Iomega=12 kg m²/s.
Detailed Explanation: This tests angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
45. JEE Main Exam-style Question: r=4 m, p=5 kg m/s perpendicular. Find L.
rpCorrect Answer: L=rp=20 kg m²/s.
Detailed Explanation: This tests particle angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
46. JEE Main Exam-style Question: I changes from 6 to 2 kg m², omega initial 4 rad/s. Find final omega.
I decreases, omega increasesCorrect Answer: I1w1=I2w2, w2=12 rad/s.
Detailed Explanation: This tests conservation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
47. JEE Main Exam-style Question: Constant torque 8 N m acts for 3 s. Change in angular momentum?
Ltslope = tauCorrect Answer: Delta L=tau t=24 kg m²/s.
Detailed Explanation: This tests torque and L. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
48. JEE Main Exam-style Question: r along +x and F along +y. Torque direction?
moment armCorrect Answer: +z by right hand rule.
Detailed Explanation: This tests vector direction. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
49. JEE Main Exam-style Question: Clockwise torque is often taken as:
moment armCorrect Answer: Negative if anticlockwise is positive.
Detailed Explanation: This tests clockwise moment. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
50. JEE Main Exam-style Question: Torque 12 N m acts on I=3 kg m². Angular acceleration?
moment armCorrect Answer: alpha=tau/I=4 rad/s².
Detailed Explanation: This tests rotational dynamics. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
12

JEE Advanced Question Bank

50 advanced questions on r×F, particle L, variable I, torque and angular momentum relation.

1. JEE Advanced Exam-style Question: For r=(2i+3j)m and F=(4i+5j)N, find z torque.
moment armCorrect Answer: tau_z=xFy-yFx=2x5-3x4=-2 N m.
Detailed Explanation: This tests r x F. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
2. JEE Advanced Exam-style Question: For r=(3i)m and p=(2j) kg m/s, find L.
rpCorrect Answer: L=6k kg m²/s.
Detailed Explanation: This tests particle angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
3. JEE Advanced Exam-style Question: A disc-student system has no external torque. If I halves, omega becomes?
I decreases, omega increasesCorrect Answer: Doubles.
Detailed Explanation: This tests conservation of angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
4. JEE Advanced Exam-style Question: If I changes slowly from I0 to I0/4 with no external torque, rotational KE changes by factor?
I decreases, omega increasesCorrect Answer: L constant, K=L²/(2I), so K becomes 4 times.
Detailed Explanation: This tests variable moment of inertia. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
5. JEE Advanced Exam-style Question: If L=at² along fixed axis, find torque.
Ltslope = tauCorrect Answer: tau=dL/dt=2at.
Detailed Explanation: This tests torque and L relation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
6. JEE Advanced Exam-style Question: Torque 10 N m acts on I=5 for 4 s from rest. Find L and omega.
Ltslope = tauCorrect Answer: L=40, omega=L/I=8 rad/s.
Detailed Explanation: This tests multi-step rotational dynamics. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
7. JEE Advanced Exam-style Question: Why is moment of a couple independent of origin?
net force 0, torque non-zeroCorrect Answer: Net force is zero, so shifting origin adds zero resultant-force moment.
Detailed Explanation: This tests couple vector. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
8. JEE Advanced Exam-style Question: r along -x and F along +y. Torque direction?
moment armCorrect Answer: -z.
Detailed Explanation: This tests right hand rule. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
9. JEE Advanced Exam-style Question: For central force, angular momentum about centre is conserved because:
rpCorrect Answer: Torque r x F is zero.
Detailed Explanation: This tests central force. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
10. JEE Advanced Exam-style Question: Planet near Sun moves faster because:
I decreases, omega increasesCorrect Answer: Angular momentum conservation with smaller radius increases tangential speed.
Detailed Explanation: This tests planetary motion. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
11. JEE Advanced Exam-style Question: For r=(2i+3j)m and F=(4i+5j)N, find z torque.
moment armCorrect Answer: tau_z=xFy-yFx=2x5-3x4=-2 N m.
Detailed Explanation: This tests r x F. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
12. JEE Advanced Exam-style Question: For r=(3i)m and p=(2j) kg m/s, find L.
rpCorrect Answer: L=6k kg m²/s.
Detailed Explanation: This tests particle angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
13. JEE Advanced Exam-style Question: A disc-student system has no external torque. If I halves, omega becomes?
I decreases, omega increasesCorrect Answer: Doubles.
Detailed Explanation: This tests conservation of angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
14. JEE Advanced Exam-style Question: If I changes slowly from I0 to I0/4 with no external torque, rotational KE changes by factor?
I decreases, omega increasesCorrect Answer: L constant, K=L²/(2I), so K becomes 4 times.
Detailed Explanation: This tests variable moment of inertia. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
15. JEE Advanced Exam-style Question: If L=at² along fixed axis, find torque.
Ltslope = tauCorrect Answer: tau=dL/dt=2at.
Detailed Explanation: This tests torque and L relation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
16. JEE Advanced Exam-style Question: Torque 10 N m acts on I=5 for 4 s from rest. Find L and omega.
Ltslope = tauCorrect Answer: L=40, omega=L/I=8 rad/s.
Detailed Explanation: This tests multi-step rotational dynamics. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
17. JEE Advanced Exam-style Question: Why is moment of a couple independent of origin?
net force 0, torque non-zeroCorrect Answer: Net force is zero, so shifting origin adds zero resultant-force moment.
Detailed Explanation: This tests couple vector. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
18. JEE Advanced Exam-style Question: r along -x and F along +y. Torque direction?
moment armCorrect Answer: -z.
Detailed Explanation: This tests right hand rule. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
19. JEE Advanced Exam-style Question: For central force, angular momentum about centre is conserved because:
rpCorrect Answer: Torque r x F is zero.
Detailed Explanation: This tests central force. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
20. JEE Advanced Exam-style Question: Planet near Sun moves faster because:
I decreases, omega increasesCorrect Answer: Angular momentum conservation with smaller radius increases tangential speed.
Detailed Explanation: This tests planetary motion. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
21. JEE Advanced Exam-style Question: For r=(2i+3j)m and F=(4i+5j)N, find z torque.
moment armCorrect Answer: tau_z=xFy-yFx=2x5-3x4=-2 N m.
Detailed Explanation: This tests r x F. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
22. JEE Advanced Exam-style Question: For r=(3i)m and p=(2j) kg m/s, find L.
rpCorrect Answer: L=6k kg m²/s.
Detailed Explanation: This tests particle angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
23. JEE Advanced Exam-style Question: A disc-student system has no external torque. If I halves, omega becomes?
I decreases, omega increasesCorrect Answer: Doubles.
Detailed Explanation: This tests conservation of angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
24. JEE Advanced Exam-style Question: If I changes slowly from I0 to I0/4 with no external torque, rotational KE changes by factor?
I decreases, omega increasesCorrect Answer: L constant, K=L²/(2I), so K becomes 4 times.
Detailed Explanation: This tests variable moment of inertia. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
25. JEE Advanced Exam-style Question: If L=at² along fixed axis, find torque.
Ltslope = tauCorrect Answer: tau=dL/dt=2at.
Detailed Explanation: This tests torque and L relation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
26. JEE Advanced Exam-style Question: Torque 10 N m acts on I=5 for 4 s from rest. Find L and omega.
Ltslope = tauCorrect Answer: L=40, omega=L/I=8 rad/s.
Detailed Explanation: This tests multi-step rotational dynamics. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
27. JEE Advanced Exam-style Question: Why is moment of a couple independent of origin?
net force 0, torque non-zeroCorrect Answer: Net force is zero, so shifting origin adds zero resultant-force moment.
Detailed Explanation: This tests couple vector. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
28. JEE Advanced Exam-style Question: r along -x and F along +y. Torque direction?
moment armCorrect Answer: -z.
Detailed Explanation: This tests right hand rule. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
29. JEE Advanced Exam-style Question: For central force, angular momentum about centre is conserved because:
rpCorrect Answer: Torque r x F is zero.
Detailed Explanation: This tests central force. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
30. JEE Advanced Exam-style Question: Planet near Sun moves faster because:
I decreases, omega increasesCorrect Answer: Angular momentum conservation with smaller radius increases tangential speed.
Detailed Explanation: This tests planetary motion. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
31. JEE Advanced Exam-style Question: For r=(2i+3j)m and F=(4i+5j)N, find z torque.
moment armCorrect Answer: tau_z=xFy-yFx=2x5-3x4=-2 N m.
Detailed Explanation: This tests r x F. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
32. JEE Advanced Exam-style Question: For r=(3i)m and p=(2j) kg m/s, find L.
rpCorrect Answer: L=6k kg m²/s.
Detailed Explanation: This tests particle angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
33. JEE Advanced Exam-style Question: A disc-student system has no external torque. If I halves, omega becomes?
I decreases, omega increasesCorrect Answer: Doubles.
Detailed Explanation: This tests conservation of angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
34. JEE Advanced Exam-style Question: If I changes slowly from I0 to I0/4 with no external torque, rotational KE changes by factor?
I decreases, omega increasesCorrect Answer: L constant, K=L²/(2I), so K becomes 4 times.
Detailed Explanation: This tests variable moment of inertia. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
35. JEE Advanced Exam-style Question: If L=at² along fixed axis, find torque.
Ltslope = tauCorrect Answer: tau=dL/dt=2at.
Detailed Explanation: This tests torque and L relation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
36. JEE Advanced Exam-style Question: Torque 10 N m acts on I=5 for 4 s from rest. Find L and omega.
Ltslope = tauCorrect Answer: L=40, omega=L/I=8 rad/s.
Detailed Explanation: This tests multi-step rotational dynamics. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
37. JEE Advanced Exam-style Question: Why is moment of a couple independent of origin?
net force 0, torque non-zeroCorrect Answer: Net force is zero, so shifting origin adds zero resultant-force moment.
Detailed Explanation: This tests couple vector. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
38. JEE Advanced Exam-style Question: r along -x and F along +y. Torque direction?
moment armCorrect Answer: -z.
Detailed Explanation: This tests right hand rule. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
39. JEE Advanced Exam-style Question: For central force, angular momentum about centre is conserved because:
rpCorrect Answer: Torque r x F is zero.
Detailed Explanation: This tests central force. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
40. JEE Advanced Exam-style Question: Planet near Sun moves faster because:
I decreases, omega increasesCorrect Answer: Angular momentum conservation with smaller radius increases tangential speed.
Detailed Explanation: This tests planetary motion. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
41. JEE Advanced Exam-style Question: For r=(2i+3j)m and F=(4i+5j)N, find z torque.
moment armCorrect Answer: tau_z=xFy-yFx=2x5-3x4=-2 N m.
Detailed Explanation: This tests r x F. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
42. JEE Advanced Exam-style Question: For r=(3i)m and p=(2j) kg m/s, find L.
rpCorrect Answer: L=6k kg m²/s.
Detailed Explanation: This tests particle angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
43. JEE Advanced Exam-style Question: A disc-student system has no external torque. If I halves, omega becomes?
I decreases, omega increasesCorrect Answer: Doubles.
Detailed Explanation: This tests conservation of angular momentum. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
44. JEE Advanced Exam-style Question: If I changes slowly from I0 to I0/4 with no external torque, rotational KE changes by factor?
I decreases, omega increasesCorrect Answer: L constant, K=L²/(2I), so K becomes 4 times.
Detailed Explanation: This tests variable moment of inertia. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
45. JEE Advanced Exam-style Question: If L=at² along fixed axis, find torque.
Ltslope = tauCorrect Answer: tau=dL/dt=2at.
Detailed Explanation: This tests torque and L relation. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
46. JEE Advanced Exam-style Question: Torque 10 N m acts on I=5 for 4 s from rest. Find L and omega.
Ltslope = tauCorrect Answer: L=40, omega=L/I=8 rad/s.
Detailed Explanation: This tests multi-step rotational dynamics. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
47. JEE Advanced Exam-style Question: Why is moment of a couple independent of origin?
net force 0, torque non-zeroCorrect Answer: Net force is zero, so shifting origin adds zero resultant-force moment.
Detailed Explanation: This tests couple vector. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
48. JEE Advanced Exam-style Question: r along -x and F along +y. Torque direction?
moment armCorrect Answer: -z.
Detailed Explanation: This tests right hand rule. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
49. JEE Advanced Exam-style Question: For central force, angular momentum about centre is conserved because:
rpCorrect Answer: Torque r x F is zero.
Detailed Explanation: This tests central force. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
50. JEE Advanced Exam-style Question: Planet near Sun moves faster because:
I decreases, omega increasesCorrect Answer: Angular momentum conservation with smaller radius increases tangential speed.
Detailed Explanation: This tests planetary motion. Draw r from pivot to point of force, use perpendicular distance or cross product, and apply angular momentum conservation only when net external torque is zero.
13

IB / IGCSE / A-Level Questions

Separate international banks with answers and explanations.

IB Questions

IB 1. Define torque.
Turning effect of a force about a point or axis.
IB 2. Torque vector formula.
tau=r x F.
IB 3. Torque magnitude.
tau=rF sin theta.
IB 4. SI unit of torque.
N m.
IB 5. Dimension of torque.
ML²T^-2.
IB 6. Moment arm meaning.
Perpendicular distance from pivot to force line of action.
IB 7. Moment of force formula.
tau=Fd.
IB 8. What is a couple?
Two equal opposite parallel forces separated by distance.
IB 9. Net force of couple.
Zero.
IB 10. Couple moment.
F times perpendicular separation.
IB 11. Angular momentum of particle.
L=r x p.
IB 12. Angular momentum of rigid body.
L=Iomega.
IB 13. Unit of angular momentum.
kg m²/s.
IB 14. Torque-angular momentum relation.
tau=dL/dt.
IB 15. Conservation condition.
Net external torque zero.
IB 16. Skater pulls arms inward.
I decreases and omega increases.
IB 17. Right-hand rule gives direction of?
Torque and angular momentum.
IB 18. Door opens easier at handle because?
Moment arm is larger.
IB 19. Wrench works by increasing?
Moment arm.
IB 20. Planet angular momentum conserved when?
Central force torque is zero.
IB 21. Gyroscope resists change due to?
Angular momentum.
IB 22. Clockwise sign convention.
Often negative if anticlockwise is positive.
IB 23. Torque can be zero if?
Force line passes through pivot or F parallel to r.
IB 24. L changes when?
External torque acts.
IB 25. Diving athlete tucks body to?
Reduce I and increase omega.

IGCSE Questions

IGCSE 1. What is moment of force?
Force times perpendicular distance from pivot.
IGCSE 2. Formula for moment.
Moment=F x d.
IGCSE 3. Unit of moment.
N m.
IGCSE 4. Door handle is far from hinge because?
Greater moment arm gives larger turning effect.
IGCSE 5. Clockwise moment direction?
Turns object clockwise.
IGCSE 6. Anticlockwise moment direction?
Turns object anticlockwise.
IGCSE 7. Balanced moments condition.
Clockwise moments equal anticlockwise moments.
IGCSE 8. What is couple?
Pair of equal opposite forces causing rotation.
IGCSE 9. Steering wheel uses?
Couple/torque.
IGCSE 10. Bottle cap opens by applying?
Torque.
IGCSE 11. Bigger force gives bigger?
Moment/torque.
IGCSE 12. Bigger distance from pivot gives bigger?
Moment/torque.
IGCSE 13. Force through pivot gives moment?
Zero.
IGCSE 14. Angular momentum basic idea.
Rotational momentum.
IGCSE 15. Spinning skater pulls arms in and spins?
Faster.
IGCSE 16. Why wrench has long handle?
To increase moment arm.
IGCSE 17. Pivot is the point about which body?
Turns.
IGCSE 18. Moment arm is measured how?
Perpendicular to line of action.
IGCSE 19. Torque is force only?
No, force and distance matter.
IGCSE 20. Right hand rule is used for?
Direction in rotation vectors.
IGCSE 21. Gyroscope is a spinning?
Rotating body.
IGCSE 22. Helicopter rotor has angular?
Momentum.
IGCSE 23. Bicycle wheel has angular?
Momentum.
IGCSE 24. Cricket bat swing involves?
Torque.
IGCSE 25. No external torque means angular momentum?
Conserved.

A-Level Questions

A-Level 1. Express torque as determinant.
tau=r x F.
A-Level 2. z component torque in 2D.
tau_z=xF_y-yF_x.
A-Level 3. Particle angular momentum.
L=r x p.
A-Level 4. Rigid body angular momentum.
L=Iomega for fixed principal axis.
A-Level 5. Torque and angular momentum.
tau=dL/dt.
A-Level 6. Conservation law.
If external torque is zero, L is constant.
A-Level 7. Couple moment independent of origin why?
Resultant force is zero.
A-Level 8. Central force torque.
Zero about force centre.
A-Level 9. Kepler second law link.
Angular momentum conservation.
A-Level 10. Rotating chair equation.
I1omega1=I2omega2.
A-Level 11. Rotational KE under L constant.
K=L²/(2I).
A-Level 12. Direction of r x F.
Right-hand rule.
A-Level 13. Torque pseudo or polar vector?
Axial vector.
A-Level 14. Angular momentum pseudo/vector type.
Axial vector.
A-Level 15. Impulse angular relation.
Angular impulse equals change in angular momentum.
A-Level 16. Angular impulse formula.
Integral tau dt.
A-Level 17. If torque constant, L changes how?
Linearly with time.
A-Level 18. Moment arm in vector form.
r sin theta.
A-Level 19. Maximum torque condition.
Force perpendicular to r.
A-Level 20. Zero torque condition.
Force parallel to r or line through pivot.
A-Level 21. Diver tucking effect.
I decreases, omega increases.
A-Level 22. Gyroscope precession cause.
External torque changes L direction.
A-Level 23. Helicopter tail rotor purpose.
Counter main rotor torque.
A-Level 24. Angular momentum dimensions.
ML²T^-1.
A-Level 25. Torque dimensions.
ML²T^-2.
14

Assertion Reason

30 assertion-reason questions.

1. Assertion: Torque is a vector. Reason: Torque is r cross F.
Answer: Both true; reason explains assertion.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
2. Assertion: Torque is maximum when force is perpendicular to radius. Reason: tau=rF sin theta.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
3. Assertion: A couple has zero net force. Reason: Forces in a couple are equal and opposite.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
4. Assertion: A couple has zero torque. Reason: Its net force is zero.
Answer: Assertion false; reason true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
5. Assertion: Angular momentum is conserved when external torque is zero. Reason: tau=dL/dt.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
6. Assertion: Door is easier to open near hinge. Reason: Moment arm is smaller near hinge.
Answer: Assertion false; reason true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
7. Assertion: Skater spins faster when arms are pulled inward. Reason: Moment of inertia decreases.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
8. Assertion: Particle angular momentum can be zero even if momentum is nonzero. Reason: If line of motion passes through origin, r x p=0.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
9. Assertion: Torque and work have same unit but different nature. Reason: Torque is vector and work is scalar.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
10. Assertion: Angular momentum of planet is conserved under central force. Reason: Central force gives zero torque about Sun.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
11. Assertion: Torque is a vector. Reason: Torque is r cross F.
Answer: Both true; reason explains assertion.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
12. Assertion: Torque is maximum when force is perpendicular to radius. Reason: tau=rF sin theta.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
13. Assertion: A couple has zero net force. Reason: Forces in a couple are equal and opposite.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
14. Assertion: A couple has zero torque. Reason: Its net force is zero.
Answer: Assertion false; reason true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
15. Assertion: Angular momentum is conserved when external torque is zero. Reason: tau=dL/dt.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
16. Assertion: Door is easier to open near hinge. Reason: Moment arm is smaller near hinge.
Answer: Assertion false; reason true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
17. Assertion: Skater spins faster when arms are pulled inward. Reason: Moment of inertia decreases.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
18. Assertion: Particle angular momentum can be zero even if momentum is nonzero. Reason: If line of motion passes through origin, r x p=0.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
19. Assertion: Torque and work have same unit but different nature. Reason: Torque is vector and work is scalar.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
20. Assertion: Angular momentum of planet is conserved under central force. Reason: Central force gives zero torque about Sun.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
21. Assertion: Torque is a vector. Reason: Torque is r cross F.
Answer: Both true; reason explains assertion.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
22. Assertion: Torque is maximum when force is perpendicular to radius. Reason: tau=rF sin theta.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
23. Assertion: A couple has zero net force. Reason: Forces in a couple are equal and opposite.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
24. Assertion: A couple has zero torque. Reason: Its net force is zero.
Answer: Assertion false; reason true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
25. Assertion: Angular momentum is conserved when external torque is zero. Reason: tau=dL/dt.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
26. Assertion: Door is easier to open near hinge. Reason: Moment arm is smaller near hinge.
Answer: Assertion false; reason true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
27. Assertion: Skater spins faster when arms are pulled inward. Reason: Moment of inertia decreases.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
28. Assertion: Particle angular momentum can be zero even if momentum is nonzero. Reason: If line of motion passes through origin, r x p=0.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
29. Assertion: Torque and work have same unit but different nature. Reason: Torque is vector and work is scalar.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
30. Assertion: Angular momentum of planet is conserved under central force. Reason: Central force gives zero torque about Sun.
Answer: Both true.
Explanation: Judge the assertion and reason separately, then decide whether the reason explains the assertion.
15

Case Study Questions

Door, wrench, skater, rotating stool, gyroscope and planetary motion cases.

Case Study: Door and moment arm
moment armPassage: A person pushes a door near and far from hinge. Questions: torque, moment arm, line of action, best angle and sign.
Questions: Identify concept, formula, direction and condition.
Answers and Detailed Explanation: Torque is Fd. Far handle and perpendicular force maximize torque.
Case Study: Wrench turning a nut
moment armPassage: A wrench rotates a nut when force is applied at the handle. Questions: why long handle, perpendicular force, torque magnitude and direction.
Questions: Identify concept, formula, direction and condition.
Answers and Detailed Explanation: Longer moment arm gives larger torque. Direction from right-hand rule.
Case Study: Ice skater
I decreases, omega increasesPassage: A spinning skater pulls arms inward. Questions: conserved quantity, change in I, change in omega, rotational KE and external torque.
Questions: Identify concept, formula, direction and condition.
Answers and Detailed Explanation: L is conserved if external torque is negligible. I decreases and omega increases.
Case Study: Rotating stool with dumbbells
I decreases, omega increasesPassage: Student on stool pulls dumbbells inward. Questions: final angular speed, energy change and condition.
Questions: Identify concept, formula, direction and condition.
Answers and Detailed Explanation: Use I1omega1=I2omega2; internal work can increase rotational KE.
Case Study: Gyroscope
Ltslope = tauPassage: A spinning wheel resists falling. Questions: angular momentum direction, external torque and precession idea.
Questions: Identify concept, formula, direction and condition.
Answers and Detailed Explanation: Torque changes direction of angular momentum rather than instantly tipping it.
Case Study: Planetary motion
I decreases, omega increasesPassage: Planet moves around Sun under central force. Questions: torque, angular momentum and speed near Sun.
Questions: Identify concept, formula, direction and condition.
Answers and Detailed Explanation: Central force produces zero torque, so angular momentum is conserved.
16

Common Student Mistakes

Avoid these common exam errors.

Torque vs Force

Torque depends on force and moment arm, not force alone.

Perpendicular Distance

Use moment arm, not always the full radius.

Wrong Sign

Choose clockwise/anticlockwise signs consistently.

Right-Hand Rule

Cross product direction decides vector direction.

L vs p

Angular momentum L is r×p, not just linear momentum.

External Torque

Conservation applies only when net external torque is zero.

Vector Nature

Torque and angular momentum require direction as well as magnitude.

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