rotational kinematics - physicstutor.kumarphysicsclasses.com

Angular Displacement

Angular displacement is the angle swept by a radius vector. Direction is given by the right hand rule.

θ = s/r1 revolution = 2π rad

Anticlockwise is usually positive.
Clockwise is usually negative.
Radian measure is dimensionless but written as rad.

Angular Velocity

Angular velocity is the rate of angular displacement. Its direction is along the axis of rotation by right hand rule.

ω = dθ/dtω_avg = Δθ/Δt

SI unit is rad/s and dimensions are T^-1.

Angular Acceleration

Angular acceleration is the rate of change of angular velocity. It may be positive or negative depending on chosen sign convention.

α = dω/dtα_avg = Δω/Δt

Same sign as omega increases angular speed; opposite sign decreases angular speed.

Rotational Equations of Motion

For constant angular acceleration, rotational motion follows the exact pattern of linear kinematics.

ω = ω₀ + αtθ = ω₀t + 1/2 αt²ω² = ω₀² + 2αθ

Linear Motion	Rotational Motion
s	θ
u	ω₀
v	ω
a	α

Relation Between Linear and Angular Variables

Very important: quantities at a point on a rotating body depend on its distance from the axis.

s = rθv = rωa_t = rαa_c = rω² = v²/r

Angular	Linear at radius r	Direction
θ	s=rθ	Arc
ω	v=rω	Tangent
α	a_t=rα	Tangent
ω²	a_c=rω²	Towards centre

Graphs

Slope and area rules are the fastest way to solve graph-based questions.

θ vs t

Slope = ω.

ω vs t

Slope = α, area = θ.

α vs t

Area = Δω.

Solved graph example: omega=2+3t from 0 to 4 s. Find theta.

Area under omega-time graph = ∫(2+3t)dt = 8+24 = 32 rad.

Important Conceptual Cases

Recognise the type of rotational motion before applying formulas.

Constant Angular Velocity

ω constant, α=0, theta increases uniformly.

Constant Angular Acceleration

Use the three rotational equations.

Increasing Angular Speed

ω and α have same sign.

Decreasing Angular Speed

ω and α have opposite signs.

Uniform Circular Motion

ω constant, a_t=0, a_c exists.

Non-Uniform Circular Motion

Both tangential and centripetal acceleration exist.

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High-Quality Numericals

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

1. CBSE angular displacement: A wheel radius 0.5 m covers arc 3 m. Find theta.

Question: A wheel radius 0.5 m covers arc 3 m. Find theta.
Diagram: shown above.
Given: Identify theta, omega, alpha, radius and time.
Formula: theta=s/r, omega=omega0+alpha t, theta=omega0t+1/2alpha t², v=r omega, a_t=r alpha, a_c=r omega².
Calculation: theta=s/r=6 rad.
Final Answer: theta=s/r=6 rad.
Exam Tip: Convert revolutions or rpm into radians before using formulas.
Common Mistake: Mixing linear and angular variables without radius.

2. NEET angular velocity: A body rotates 40 rad in 8 s. Find average omega.

Question: A body rotates 40 rad in 8 s. Find average omega.
Diagram: shown above.
Given: Identify theta, omega, alpha, radius and time.
Formula: theta=s/r, omega=omega0+alpha t, theta=omega0t+1/2alpha t², v=r omega, a_t=r alpha, a_c=r omega².
Calculation: omega=5 rad/s.
Final Answer: omega=5 rad/s.
Exam Tip: Convert revolutions or rpm into radians before using formulas.
Common Mistake: Mixing linear and angular variables without radius.

3. JEE Main angular acceleration: omega changes from 5 to 25 rad/s in 4 s.

Question: omega changes from 5 to 25 rad/s in 4 s.
Diagram: shown above.
Given: Identify theta, omega, alpha, radius and time.
Formula: theta=s/r, omega=omega0+alpha t, theta=omega0t+1/2alpha t², v=r omega, a_t=r alpha, a_c=r omega².
Calculation: alpha=5 rad/s².
Final Answer: alpha=5 rad/s².
Exam Tip: Convert revolutions or rpm into radians before using formulas.
Common Mistake: Mixing linear and angular variables without radius.

4. JEE Advanced equations: omega0=2, alpha=3, t=4. Find theta.

Question: omega0=2, alpha=3, t=4. Find theta.
Diagram: shown above.
Given: Identify theta, omega, alpha, radius and time.
Formula: theta=s/r, omega=omega0+alpha t, theta=omega0t+1/2alpha t², v=r omega, a_t=r alpha, a_c=r omega².
Calculation: theta=2x4+1/2x3x16=32 rad.
Final Answer: theta=2x4+1/2x3x16=32 rad.
Exam Tip: Convert revolutions or rpm into radians before using formulas.
Common Mistake: Mixing linear and angular variables without radius.

5. IB linear speed: r=0.4 m, omega=15 rad/s. Find v.

Question: r=0.4 m, omega=15 rad/s. Find v.
Diagram: shown above.
Given: Identify theta, omega, alpha, radius and time.
Formula: theta=s/r, omega=omega0+alpha t, theta=omega0t+1/2alpha t², v=r omega, a_t=r alpha, a_c=r omega².
Calculation: v=6 m/s.
Final Answer: v=6 m/s.
Exam Tip: Convert revolutions or rpm into radians before using formulas.
Common Mistake: Mixing linear and angular variables without radius.

6. IGCSE revolution: A wheel makes 3 revolutions. Find theta.

Question: A wheel makes 3 revolutions. Find theta.
Diagram: shown above.
Given: Identify theta, omega, alpha, radius and time.
Formula: theta=s/r, omega=omega0+alpha t, theta=omega0t+1/2alpha t², v=r omega, a_t=r alpha, a_c=r omega².
Calculation: theta=6pi rad.
Final Answer: theta=6pi rad.
Exam Tip: Convert revolutions or rpm into radians before using formulas.
Common Mistake: Mixing linear and angular variables without radius.

7. A-Level graph: omega=4+2t from 0 to 5 s. Find theta.

Question: omega=4+2t from 0 to 5 s. Find theta.
Diagram: shown above.
Given: Identify theta, omega, alpha, radius and time.
Formula: theta=s/r, omega=omega0+alpha t, theta=omega0t+1/2alpha t², v=r omega, a_t=r alpha, a_c=r omega².
Calculation: theta=integral(4+2t)dt=20+25=45 rad.
Final Answer: theta=integral(4+2t)dt=20+25=45 rad.
Exam Tip: Convert revolutions or rpm into radians before using formulas.
Common Mistake: Mixing linear and angular variables without radius.

8. Centripetal acceleration: r=2 m and omega=3 rad/s. Find a_c.

Question: r=2 m and omega=3 rad/s. Find a_c.
Diagram: shown above.
Given: Identify theta, omega, alpha, radius and time.
Formula: theta=s/r, omega=omega0+alpha t, theta=omega0t+1/2alpha t², v=r omega, a_t=r alpha, a_c=r omega².
Calculation: a_c=18 m/s².
Final Answer: a_c=18 m/s².
Exam Tip: Convert revolutions or rpm into radians before using formulas.
Common Mistake: Mixing linear and angular variables without radius.

9. Tangential acceleration: r=0.25 m and alpha=12 rad/s². Find a_t.

Question: r=0.25 m and alpha=12 rad/s². Find a_t.
Diagram: shown above.
Given: Identify theta, omega, alpha, radius and time.
Formula: theta=s/r, omega=omega0+alpha t, theta=omega0t+1/2alpha t², v=r omega, a_t=r alpha, a_c=r omega².
Calculation: a_t=3 m/s².
Final Answer: a_t=3 m/s².
Exam Tip: Convert revolutions or rpm into radians before using formulas.
Common Mistake: Mixing linear and angular variables without radius.

10. RPM conversion: A fan rotates at 300 rpm. Find omega.

Question: A fan rotates at 300 rpm. Find omega.
Diagram: shown above.
Given: Identify theta, omega, alpha, radius and time.
Formula: theta=s/r, omega=omega0+alpha t, theta=omega0t+1/2alpha t², v=r omega, a_t=r alpha, a_c=r omega².
Calculation: 300 rpm=5 rps=10pi rad/s.
Final Answer: 300 rpm=5 rps=10pi rad/s.
Exam Tip: Convert revolutions or rpm into radians before using formulas.
Common Mistake: Mixing linear and angular variables without radius.

NEET Question Bank

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

1. NEET Exam-style Question: If arc length is 2 m and radius is 0.5 m, angular displacement is: A 1 rad B 2 rad C 4 rad D 8 rad

Correct Answer: C. theta=s/r=4 rad.
Detailed Explanation: This tests angular displacement. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

2. NEET Exam-style Question: One revolution equals: A pi rad B 2pi rad C 180 rad D 1 rad

Correct Answer: B. 1 revolution=2pi rad.
Detailed Explanation: This tests radian conversion. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

3. NEET Exam-style Question: A wheel covers 20 rad in 5 s. Average angular velocity is: A 2 B 4 C 10 D 25 rad/s

Correct Answer: B. omega=Delta theta/Delta t=4 rad/s.
Detailed Explanation: This tests angular velocity. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

4. NEET Exam-style Question: Angular speed changes from 2 to 10 rad/s in 4 s. alpha is: A 1 B 2 C 3 D 4 rad/s²

Correct Answer: B. alpha=Delta omega/t=2 rad/s².
Detailed Explanation: This tests angular acceleration. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

5. NEET Exam-style Question: If r=0.5 m and omega=10 rad/s, speed is: A 2 B 5 C 10 D 20 m/s

Correct Answer: B. v=r omega=5 m/s.
Detailed Explanation: This tests linear-angular relation. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

6. NEET Exam-style Question: For omega=4 rad/s, r=2 m, a_c is: A 8 B 16 C 32 D 64 m/s²

Correct Answer: C. a_c=r omega²=32.
Detailed Explanation: This tests centripetal acceleration. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

7. NEET Exam-style Question: For constant alpha, omega equals: A omega0+alpha t B omega0-alpha/t C alpha/theta D theta/t

Correct Answer: A.
Detailed Explanation: This tests equation. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

8. NEET Exam-style Question: Slope of theta-time graph gives: A alpha B omega C torque D energy

Correct Answer: B.
Detailed Explanation: This tests graph. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

9. NEET Exam-style Question: Area under omega-time graph gives: A theta B alpha C radius D mass

Correct Answer: A.
Detailed Explanation: This tests graph. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

10. NEET Exam-style Question: In uniform circular motion, angular speed is constant but acceleration is: A zero B centripetal C tangential only D none

Correct Answer: B.
Detailed Explanation: This tests uniform circular motion. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

11. NEET Exam-style Question: If arc length is 2 m and radius is 0.5 m, angular displacement is: A 1 rad B 2 rad C 4 rad D 8 rad

12. NEET Exam-style Question: One revolution equals: A pi rad B 2pi rad C 180 rad D 1 rad

13. NEET Exam-style Question: A wheel covers 20 rad in 5 s. Average angular velocity is: A 2 B 4 C 10 D 25 rad/s

14. NEET Exam-style Question: Angular speed changes from 2 to 10 rad/s in 4 s. alpha is: A 1 B 2 C 3 D 4 rad/s²

15. NEET Exam-style Question: If r=0.5 m and omega=10 rad/s, speed is: A 2 B 5 C 10 D 20 m/s

16. NEET Exam-style Question: For omega=4 rad/s, r=2 m, a_c is: A 8 B 16 C 32 D 64 m/s²

17. NEET Exam-style Question: For constant alpha, omega equals: A omega0+alpha t B omega0-alpha/t C alpha/theta D theta/t

18. NEET Exam-style Question: Slope of theta-time graph gives: A alpha B omega C torque D energy

19. NEET Exam-style Question: Area under omega-time graph gives: A theta B alpha C radius D mass

20. NEET Exam-style Question: In uniform circular motion, angular speed is constant but acceleration is: A zero B centripetal C tangential only D none

21. NEET Exam-style Question: If arc length is 2 m and radius is 0.5 m, angular displacement is: A 1 rad B 2 rad C 4 rad D 8 rad

22. NEET Exam-style Question: One revolution equals: A pi rad B 2pi rad C 180 rad D 1 rad

23. NEET Exam-style Question: A wheel covers 20 rad in 5 s. Average angular velocity is: A 2 B 4 C 10 D 25 rad/s

24. NEET Exam-style Question: Angular speed changes from 2 to 10 rad/s in 4 s. alpha is: A 1 B 2 C 3 D 4 rad/s²

25. NEET Exam-style Question: If r=0.5 m and omega=10 rad/s, speed is: A 2 B 5 C 10 D 20 m/s

26. NEET Exam-style Question: For omega=4 rad/s, r=2 m, a_c is: A 8 B 16 C 32 D 64 m/s²

27. NEET Exam-style Question: For constant alpha, omega equals: A omega0+alpha t B omega0-alpha/t C alpha/theta D theta/t

28. NEET Exam-style Question: Slope of theta-time graph gives: A alpha B omega C torque D energy

29. NEET Exam-style Question: Area under omega-time graph gives: A theta B alpha C radius D mass

30. NEET Exam-style Question: In uniform circular motion, angular speed is constant but acceleration is: A zero B centripetal C tangential only D none

31. NEET Exam-style Question: If arc length is 2 m and radius is 0.5 m, angular displacement is: A 1 rad B 2 rad C 4 rad D 8 rad

32. NEET Exam-style Question: One revolution equals: A pi rad B 2pi rad C 180 rad D 1 rad

33. NEET Exam-style Question: A wheel covers 20 rad in 5 s. Average angular velocity is: A 2 B 4 C 10 D 25 rad/s

34. NEET Exam-style Question: Angular speed changes from 2 to 10 rad/s in 4 s. alpha is: A 1 B 2 C 3 D 4 rad/s²

35. NEET Exam-style Question: If r=0.5 m and omega=10 rad/s, speed is: A 2 B 5 C 10 D 20 m/s

36. NEET Exam-style Question: For omega=4 rad/s, r=2 m, a_c is: A 8 B 16 C 32 D 64 m/s²

37. NEET Exam-style Question: For constant alpha, omega equals: A omega0+alpha t B omega0-alpha/t C alpha/theta D theta/t

38. NEET Exam-style Question: Slope of theta-time graph gives: A alpha B omega C torque D energy

39. NEET Exam-style Question: Area under omega-time graph gives: A theta B alpha C radius D mass

40. NEET Exam-style Question: In uniform circular motion, angular speed is constant but acceleration is: A zero B centripetal C tangential only D none

41. NEET Exam-style Question: If arc length is 2 m and radius is 0.5 m, angular displacement is: A 1 rad B 2 rad C 4 rad D 8 rad

42. NEET Exam-style Question: One revolution equals: A pi rad B 2pi rad C 180 rad D 1 rad

43. NEET Exam-style Question: A wheel covers 20 rad in 5 s. Average angular velocity is: A 2 B 4 C 10 D 25 rad/s

44. NEET Exam-style Question: Angular speed changes from 2 to 10 rad/s in 4 s. alpha is: A 1 B 2 C 3 D 4 rad/s²

45. NEET Exam-style Question: If r=0.5 m and omega=10 rad/s, speed is: A 2 B 5 C 10 D 20 m/s

46. NEET Exam-style Question: For omega=4 rad/s, r=2 m, a_c is: A 8 B 16 C 32 D 64 m/s²

47. NEET Exam-style Question: For constant alpha, omega equals: A omega0+alpha t B omega0-alpha/t C alpha/theta D theta/t

48. NEET Exam-style Question: Slope of theta-time graph gives: A alpha B omega C torque D energy

49. NEET Exam-style Question: Area under omega-time graph gives: A theta B alpha C radius D mass

50. NEET Exam-style Question: In uniform circular motion, angular speed is constant but acceleration is: A zero B centripetal C tangential only D none

JEE Main Question Bank

50 difficult JEE Main-style questions.

1. JEE Main Exam-style Question: A wheel starts from rest with alpha=2 rad/s² for 5 s. Find omega.

Correct Answer: omega=omega0+alpha t=10 rad/s.
Detailed Explanation: This tests rotational equations. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

2. JEE Main Exam-style Question: Same wheel: angular displacement in 5 s.

Correct Answer: theta=1/2 alpha t²=25 rad.
Detailed Explanation: This tests angular displacement. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

3. JEE Main Exam-style Question: A point 0.2 m from axis has omega=30 rad/s. Find v.

Correct Answer: v=r omega=6 m/s.
Detailed Explanation: This tests linear-angular relation. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

4. JEE Main Exam-style Question: For v=10 m/s and r=2 m, find a_c.

Correct Answer: a_c=v²/r=50 m/s².
Detailed Explanation: This tests centripetal acceleration. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

5. JEE Main Exam-style Question: Area under alpha-t graph is 12 rad/s. What changes?

Correct Answer: Change in angular velocity.
Detailed Explanation: This tests graph interpretation. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

6. JEE Main Exam-style Question: omega positive and alpha negative means angular speed is:

Correct Answer: Decreasing if omega and alpha are opposite.
Detailed Explanation: This tests sign convention. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

7. JEE Main Exam-style Question: Find angular speed for 120 rpm.

Correct Answer: 120 rpm=2 rev/s=4pi rad/s.
Detailed Explanation: This tests radian conversion. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

8. JEE Main Exam-style Question: Fan from rest reaches 60 rad/s in 10 s. Find alpha and theta.

Correct Answer: alpha=6 rad/s², theta=300 rad.
Detailed Explanation: This tests multi-step. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

9. JEE Main Exam-style Question: A wheel rolls without slipping with v=8 m/s and r=0.4 m. Find omega.

Correct Answer: omega=v/r=20 rad/s.
Detailed Explanation: This tests mixed motion. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

10. JEE Main Exam-style Question: Slope of omega-t graph is constant positive. Motion has:

Correct Answer: Constant positive angular acceleration.
Detailed Explanation: This tests graph. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

11. JEE Main Exam-style Question: A wheel starts from rest with alpha=2 rad/s² for 5 s. Find omega.

12. JEE Main Exam-style Question: Same wheel: angular displacement in 5 s.

13. JEE Main Exam-style Question: A point 0.2 m from axis has omega=30 rad/s. Find v.

14. JEE Main Exam-style Question: For v=10 m/s and r=2 m, find a_c.

15. JEE Main Exam-style Question: Area under alpha-t graph is 12 rad/s. What changes?

16. JEE Main Exam-style Question: omega positive and alpha negative means angular speed is:

17. JEE Main Exam-style Question: Find angular speed for 120 rpm.

18. JEE Main Exam-style Question: Fan from rest reaches 60 rad/s in 10 s. Find alpha and theta.

19. JEE Main Exam-style Question: A wheel rolls without slipping with v=8 m/s and r=0.4 m. Find omega.

20. JEE Main Exam-style Question: Slope of omega-t graph is constant positive. Motion has:

21. JEE Main Exam-style Question: A wheel starts from rest with alpha=2 rad/s² for 5 s. Find omega.

22. JEE Main Exam-style Question: Same wheel: angular displacement in 5 s.

23. JEE Main Exam-style Question: A point 0.2 m from axis has omega=30 rad/s. Find v.

24. JEE Main Exam-style Question: For v=10 m/s and r=2 m, find a_c.

25. JEE Main Exam-style Question: Area under alpha-t graph is 12 rad/s. What changes?

26. JEE Main Exam-style Question: omega positive and alpha negative means angular speed is:

27. JEE Main Exam-style Question: Find angular speed for 120 rpm.

28. JEE Main Exam-style Question: Fan from rest reaches 60 rad/s in 10 s. Find alpha and theta.

29. JEE Main Exam-style Question: A wheel rolls without slipping with v=8 m/s and r=0.4 m. Find omega.

30. JEE Main Exam-style Question: Slope of omega-t graph is constant positive. Motion has:

31. JEE Main Exam-style Question: A wheel starts from rest with alpha=2 rad/s² for 5 s. Find omega.

32. JEE Main Exam-style Question: Same wheel: angular displacement in 5 s.

33. JEE Main Exam-style Question: A point 0.2 m from axis has omega=30 rad/s. Find v.

34. JEE Main Exam-style Question: For v=10 m/s and r=2 m, find a_c.

35. JEE Main Exam-style Question: Area under alpha-t graph is 12 rad/s. What changes?

36. JEE Main Exam-style Question: omega positive and alpha negative means angular speed is:

37. JEE Main Exam-style Question: Find angular speed for 120 rpm.

38. JEE Main Exam-style Question: Fan from rest reaches 60 rad/s in 10 s. Find alpha and theta.

39. JEE Main Exam-style Question: A wheel rolls without slipping with v=8 m/s and r=0.4 m. Find omega.

40. JEE Main Exam-style Question: Slope of omega-t graph is constant positive. Motion has:

41. JEE Main Exam-style Question: A wheel starts from rest with alpha=2 rad/s² for 5 s. Find omega.

42. JEE Main Exam-style Question: Same wheel: angular displacement in 5 s.

43. JEE Main Exam-style Question: A point 0.2 m from axis has omega=30 rad/s. Find v.

44. JEE Main Exam-style Question: For v=10 m/s and r=2 m, find a_c.

45. JEE Main Exam-style Question: Area under alpha-t graph is 12 rad/s. What changes?

46. JEE Main Exam-style Question: omega positive and alpha negative means angular speed is:

47. JEE Main Exam-style Question: Find angular speed for 120 rpm.

48. JEE Main Exam-style Question: Fan from rest reaches 60 rad/s in 10 s. Find alpha and theta.

49. JEE Main Exam-style Question: A wheel rolls without slipping with v=8 m/s and r=0.4 m. Find omega.

50. JEE Main Exam-style Question: Slope of omega-t graph is constant positive. Motion has:

JEE Advanced Question Bank

50 advanced questions on equations, graphs and mixed linear-rotational relations.

1. JEE Advanced Exam-style Question: A disc has omega0=4 rad/s, alpha=3 rad/s². Find theta in 6 s.

Correct Answer: theta=omega0 t+1/2 alpha t²=24+54=78 rad.
Detailed Explanation: This tests rotational equations. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

2. JEE Advanced Exam-style Question: omega-t graph is omega=2+3t. Find angular displacement from 0 to 4 s.

Correct Answer: theta=integral(2+3t)dt=8+24=32 rad.
Detailed Explanation: This tests graphs. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

3. JEE Advanced Exam-style Question: Two points on same rigid body at radii r and 2r. Compare speeds.

Correct Answer: v proportional to r, so ratio 1:2.
Detailed Explanation: This tests mixed linear-rotational. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

4. JEE Advanced Exam-style Question: If alpha=kt, omega change from 0 to T?

Correct Answer: Delta omega=integral kt dt=kT²/2.
Detailed Explanation: This tests angular acceleration. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

5. JEE Advanced Exam-style Question: For r=0.5, omega=6, alpha=8, find total acceleration.

Correct Answer: a_c=18, a_t=4, total=sqrt(18²+4²) m/s².
Detailed Explanation: This tests centripetal and tangential. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

6. JEE Advanced Exam-style Question: Wheel slows from 40 to 10 rad/s over 150 rad. Find alpha.

Correct Answer: omega²=omega0²+2alpha theta, alpha=(100-1600)/300=-5 rad/s².
Detailed Explanation: This tests multi-step. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

7. JEE Advanced Exam-style Question: alpha-t graph triangular with base 6 s and height 4 rad/s². Find Delta omega.

Correct Answer: Area=12 rad/s.
Detailed Explanation: This tests graph area. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

8. JEE Advanced Exam-style Question: A particle travels 3 m on circle radius 0.75 m. Find theta in revolutions.

Correct Answer: theta=4 rad=4/(2pi) rev.
Detailed Explanation: This tests radian relation. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

9. JEE Advanced Exam-style Question: A wheel has angular acceleration 5 rad/s² and radius 0.3 m. Tangential acceleration?

Correct Answer: a_t=r alpha=1.5 m/s².
Detailed Explanation: This tests rolling link. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

10. JEE Advanced Exam-style Question: If speed changes on circular path, acceleration components are:

Correct Answer: Tangential plus centripetal components.
Detailed Explanation: This tests non-uniform circular motion. Convert revolutions to radians, choose sign convention, and use the rotational formula exactly like the matching linear kinematics formula.

11. JEE Advanced Exam-style Question: A disc has omega0=4 rad/s, alpha=3 rad/s². Find theta in 6 s.

12. JEE Advanced Exam-style Question: omega-t graph is omega=2+3t. Find angular displacement from 0 to 4 s.

13. JEE Advanced Exam-style Question: Two points on same rigid body at radii r and 2r. Compare speeds.

14. JEE Advanced Exam-style Question: If alpha=kt, omega change from 0 to T?

15. JEE Advanced Exam-style Question: For r=0.5, omega=6, alpha=8, find total acceleration.

16. JEE Advanced Exam-style Question: Wheel slows from 40 to 10 rad/s over 150 rad. Find alpha.

17. JEE Advanced Exam-style Question: alpha-t graph triangular with base 6 s and height 4 rad/s². Find Delta omega.

18. JEE Advanced Exam-style Question: A particle travels 3 m on circle radius 0.75 m. Find theta in revolutions.

19. JEE Advanced Exam-style Question: A wheel has angular acceleration 5 rad/s² and radius 0.3 m. Tangential acceleration?

20. JEE Advanced Exam-style Question: If speed changes on circular path, acceleration components are:

21. JEE Advanced Exam-style Question: A disc has omega0=4 rad/s, alpha=3 rad/s². Find theta in 6 s.

22. JEE Advanced Exam-style Question: omega-t graph is omega=2+3t. Find angular displacement from 0 to 4 s.

23. JEE Advanced Exam-style Question: Two points on same rigid body at radii r and 2r. Compare speeds.

24. JEE Advanced Exam-style Question: If alpha=kt, omega change from 0 to T?

25. JEE Advanced Exam-style Question: For r=0.5, omega=6, alpha=8, find total acceleration.

26. JEE Advanced Exam-style Question: Wheel slows from 40 to 10 rad/s over 150 rad. Find alpha.

27. JEE Advanced Exam-style Question: alpha-t graph triangular with base 6 s and height 4 rad/s². Find Delta omega.

28. JEE Advanced Exam-style Question: A particle travels 3 m on circle radius 0.75 m. Find theta in revolutions.

29. JEE Advanced Exam-style Question: A wheel has angular acceleration 5 rad/s² and radius 0.3 m. Tangential acceleration?

30. JEE Advanced Exam-style Question: If speed changes on circular path, acceleration components are:

31. JEE Advanced Exam-style Question: A disc has omega0=4 rad/s, alpha=3 rad/s². Find theta in 6 s.

32. JEE Advanced Exam-style Question: omega-t graph is omega=2+3t. Find angular displacement from 0 to 4 s.

33. JEE Advanced Exam-style Question: Two points on same rigid body at radii r and 2r. Compare speeds.

34. JEE Advanced Exam-style Question: If alpha=kt, omega change from 0 to T?

35. JEE Advanced Exam-style Question: For r=0.5, omega=6, alpha=8, find total acceleration.

36. JEE Advanced Exam-style Question: Wheel slows from 40 to 10 rad/s over 150 rad. Find alpha.

37. JEE Advanced Exam-style Question: alpha-t graph triangular with base 6 s and height 4 rad/s². Find Delta omega.

38. JEE Advanced Exam-style Question: A particle travels 3 m on circle radius 0.75 m. Find theta in revolutions.

39. JEE Advanced Exam-style Question: A wheel has angular acceleration 5 rad/s² and radius 0.3 m. Tangential acceleration?

40. JEE Advanced Exam-style Question: If speed changes on circular path, acceleration components are:

41. JEE Advanced Exam-style Question: A disc has omega0=4 rad/s, alpha=3 rad/s². Find theta in 6 s.

42. JEE Advanced Exam-style Question: omega-t graph is omega=2+3t. Find angular displacement from 0 to 4 s.

43. JEE Advanced Exam-style Question: Two points on same rigid body at radii r and 2r. Compare speeds.

44. JEE Advanced Exam-style Question: If alpha=kt, omega change from 0 to T?

45. JEE Advanced Exam-style Question: For r=0.5, omega=6, alpha=8, find total acceleration.

46. JEE Advanced Exam-style Question: Wheel slows from 40 to 10 rad/s over 150 rad. Find alpha.

47. JEE Advanced Exam-style Question: alpha-t graph triangular with base 6 s and height 4 rad/s². Find Delta omega.

48. JEE Advanced Exam-style Question: A particle travels 3 m on circle radius 0.75 m. Find theta in revolutions.

49. JEE Advanced Exam-style Question: A wheel has angular acceleration 5 rad/s² and radius 0.3 m. Tangential acceleration?

50. JEE Advanced Exam-style Question: If speed changes on circular path, acceleration components are:

IB / IGCSE / A-Level Questions

Separate international banks with answers and explanations.

IB Questions

IB 1. Define angular displacement.

Angle swept by radius vector, measured in radians.

IB 2. State theta=s/r.

Angular displacement equals arc length divided by radius.

IB 3. One revolution in radians.

2pi rad.

IB 4. Average angular velocity.

Delta theta / Delta t.

IB 5. Instantaneous angular velocity.

dtheta/dt.

IB 6. Angular velocity unit.

rad/s.

IB 7. Angular acceleration definition.

domega/dt.

IB 8. Angular acceleration unit.

rad/s².

IB 9. Direction of angular velocity.

Right-hand rule.

IB 10. Relation v and omega.

v=r omega.

IB 11. Tangential acceleration.

a_t=r alpha.

IB 12. Centripetal acceleration.

a_c=r omega²=v²/r.

IB 13. Slope theta-t graph.

Angular velocity.

IB 14. Slope omega-t graph.

Angular acceleration.

IB 15. Area under omega-t graph.

Angular displacement.

IB 16. Area under alpha-t graph.

Change in angular velocity.

IB 17. Uniform circular motion alpha.

Zero if angular speed is constant.

IB 18. Non-uniform circular motion.

Has tangential and centripetal acceleration.

IB 19. Why radians are useful?

They make s=r theta valid directly.

IB 20. Positive rotation convention.

Usually anticlockwise positive unless stated.

IB 21. Equation omega=omega0+alpha t condition.

Constant angular acceleration.

IB 22. Equation theta=omega0t+1/2alpha t² condition.

Constant angular acceleration.

IB 23. Equation omega²=omega0²+2alpha theta condition.

Constant angular acceleration.

IB 24. Linear-rotational analogy for s.

theta.

IB 25. Linear-rotational analogy for a.

alpha.

IGCSE Questions

IGCSE 1. What is one full turn?

One revolution.

IGCSE 2. One revolution in degrees.

360 degrees.

IGCSE 3. One revolution in radians.

2pi radians.

IGCSE 4. What is angular speed?

Angle turned per second.

IGCSE 5. Angular speed unit.

rad/s.

IGCSE 6. A wheel turns 10 rad in 2 s. Angular speed?

5 rad/s.

IGCSE 7. Arc length formula.

s=r theta.

IGCSE 8. Speed at rim formula.

v=r omega.

IGCSE 9. Centre of wheel speed due to rotation?

Zero for pure rotation about fixed axis.

IGCSE 10. Point farther from axis has more?

Linear speed.

IGCSE 11. Uniform circular motion speed.

Constant speed.

IGCSE 12. Uniform circular motion acceleration direction.

Towards centre.

IGCSE 13. Clock hands have angular motion?

Yes.

IGCSE 14. Fan starting up has angular acceleration?

Positive angular acceleration.

IGCSE 15. Fan slowing down has angular acceleration opposite?

Angular velocity direction.

IGCSE 16. Graph slope means?

Rate of change.

IGCSE 17. Area under speed-time graph means?

Displacement; similarly omega-time area gives angle.

IGCSE 18. Angular displacement symbol.

theta.

IGCSE 19. Angular velocity symbol.

omega.

IGCSE 20. Angular acceleration symbol.

alpha.

IGCSE 21. Radius unit.

metre.

IGCSE 22. Radian is dimensionless?

Yes.

IGCSE 23. Tangential direction is along?

Tangent to circle.

IGCSE 24. Centripetal direction is toward?

Centre.

IGCSE 25. Bicycle wheel example of?

Rotational motion.

A-Level Questions

A-Level 1. Differentiate theta to get omega.

omega=dtheta/dt.

A-Level 2. Differentiate omega to get alpha.

alpha=domega/dt.

A-Level 3. Integrate omega over time.

theta=integral omega dt.

A-Level 4. Integrate alpha over time.

Delta omega=integral alpha dt.

A-Level 5. Derive v=r omega.

Differentiate s=r theta with respect to time.

A-Level 6. Derive a_t=r alpha.

Differentiate v=r omega.

A-Level 7. Centripetal acceleration in angular form.

a_c=r omega².

A-Level 8. Total acceleration for non-uniform circular motion.

sqrt(a_t²+a_c²).

A-Level 9. Condition for constant angular acceleration equations.

alpha constant.

A-Level 10. omega-theta relation.

omega²=omega0²+2alpha theta.

A-Level 11. Graph theta-t curvature indicates.

Changing angular velocity.

A-Level 12. Graph omega-t slope.

Angular acceleration.

A-Level 13. Graph alpha-t area.

Change in angular velocity.

A-Level 14. Convert rpm to rad/s.

multiply rpm by 2pi/60.

A-Level 15. Convert rad/s to rpm.

multiply by 60/(2pi).

A-Level 16. Angular velocity vector direction.

Along axis by right-hand rule.

A-Level 17. Clockwise vs anticlockwise signs.

Depend on chosen positive convention.

A-Level 18. Rigid body same omega?

All points share same angular velocity.

A-Level 19. Rigid body different linear speeds?

v proportional to radius.

A-Level 20. Uniform circular motion alpha.

Zero for constant omega.

A-Level 21. Non-uniform circular motion alpha.

Nonzero when omega changes.

A-Level 22. SI unit of theta.

Radian.

A-Level 23. Dimension of omega.

T^-1.

A-Level 24. Dimension of alpha.

T^-2.

A-Level 25. Radian measure advantage.

Arc formulas become direct.

Assertion Reason

30 assertion-reason questions.

1. Assertion: Angular displacement is measured in radians. Reason: theta=s/r.

Answer: Both true; reason explains radian measure.
Explanation: Check both statements and whether the reason correctly explains the assertion.

2. Assertion: All points of a rigid body have same angular speed. Reason: They complete one revolution in the same time.