JEE Main - Equations of rotational motion and comparison with linear motion Online Test (MCQ Quiz)

1. Which of the following is the rotational analogue of linear velocity?

A) Angular acceleration B) Torque C) Angular velocity D) Moment of inertia

2. The SI unit of angular velocity is:

A) m/s B) rad/s C) m/s^2 D) rad/s^2

3. Which physical quantity is the rotational analogue of linear acceleration?

A) Angular momentum B) Torque C) Angular velocity D) Angular acceleration

4. The SI unit of angular acceleration is:

A) rad/s B) rad/s^2 C) N.m D) kg.m^2

5. Which of the following equations represents the rotational analogue of Newton's second law of motion (F=ma)?

A) τ = Iα B) L = Iω C) E = Iω^2 D) P = τω

6. In the equation τ = Iα, what does 'I' represent?

A) Linear inertia B) Angular acceleration C) Moment of inertia D) Torque

7. Which quantity is the rotational analogue of mass?

A) Moment of inertia B) Torque C) Angular momentum D) Angular acceleration

8. The rotational analogue of linear momentum (p=mv) is:

A) Angular impulse B) Angular momentum (L=Iω) C) Torque (τ=Iα) D) Angular kinetic energy (E=1/2 Iω^2)

9. Which equation correctly compares the rotational kinetic energy to linear kinetic energy?

A) KE_rotational = 1/2 Iω^2 and KE_linear = 1/2 mv^2 B) KE_rotational = Iω and KE_linear = mv C) KE_rotational = 1/2 τθ and KE_linear = 1/2 Fd D) KE_rotational = Iα and KE_linear = ma

10. The rotational analogue of displacement (s) is:

A) Angular velocity (ω) B) Angular acceleration (α) C) Angular displacement (θ) D) Torque (τ)

11. Which equation represents the rotational analogue of the first equation of linear motion (v = u + at)?

A) ω_f = ω_i + αt B) θ = ω_i t + 1/2 αt^2 C) ω_f^2 = ω_i^2 + 2αθ D) ω = θ/t

12. The rotational equivalent of the second linear equation of motion (s = ut + 1/2 at^2) is:

A) θ = ω_f t - 1/2 αt^2 B) ω_f = ω_i + αt C) θ = ω_i t + 1/2 αt^2 D) ω_f^2 = ω_i^2 + 2αθ

13. Which equation compares to the third linear equation of motion (v^2 = u^2 + 2as) in rotational dynamics?

A) ω_f = ω_i + αt B) θ = ω_i t + 1/2 αt^2 C) ω_f^2 = ω_i^2 + 2αθ D) ω_f = ω_i + 2αθ

14. The rotational analogue of force (F) is:

A) Moment of inertia (I) B) Angular acceleration (α) C) Torque (τ) D) Angular velocity (ω)

15. If a net torque acts on a rigid body, it causes:

A) Constant angular velocity B) Uniform linear motion C) Angular acceleration D) Linear acceleration

16. Which quantity is conserved if no external torque acts on a system?

A) Angular momentum B) Angular velocity C) Angular acceleration D) Moment of inertia

17. The rotational analogue of impulse (J = FΔt) is:

A) Angular impulse (τΔt) B) Torque (τ) C) Angular momentum (L) D) Angular kinetic energy

18. The work done in rotational motion is given by W = τΔθ. What is the linear analogue of this equation?

A) W = Fs B) W = ma C) W = mv D) W = Fd

19. Power in rotational motion is given by P = τω. What is the linear analogue of this equation?

A) P = Fv B) P = ma C) P = F/v D) P = Fd

20. If the moment of inertia of a body decreases, and its angular momentum remains constant, what happens to its angular velocity?

A) Decreases B) Increases C) Remains the same D) Becomes zero

21. Which of the following is NOT a valid equation of rotational motion under constant angular acceleration?

A) ω_f = ω_i + αt B) θ = ω_i t + 1/2 αt^2 C) ω_f^2 = ω_i^2 + 2αθ D) ω_f = ω_i + αt^2

22. The relationship between angular velocity (ω) and linear velocity (v) for a point at a distance r from the axis of rotation is:

A) v = ω/r B) v = ωr C) v = ω^2 r D) v = ω + r

23. The relationship between angular acceleration (α) and linear acceleration (a) for a point at a distance r from the axis of rotation is:

A) a = α/r B) a = αr C) a = α^2 r D) a = α + r

24. If a body is rotating with constant angular velocity, what is its angular acceleration?

A) Non-zero B) Zero C) Infinite D) Cannot be determined

25. Which quantity represents the 'effort' required to change the rotational state of motion of a body?

A) Moment of inertia B) Angular momentum C) Torque D) Angular acceleration

26. The equation τ = dL/dt directly relates:

A) Torque and angular acceleration B) Torque and angular momentum C) Moment of inertia and angular velocity D) Angular velocity and angular displacement

27. Consider a rigid body rotating about a fixed axis. If the net external torque is zero, then:

A) Angular velocity is zero B) Angular acceleration is zero C) Moment of inertia is zero D) Angular momentum is not conserved

28. The unit of angular impulse is equivalent to the unit of:

A) Torque B) Angular momentum C) Moment of inertia D) Angular kinetic energy

29. Which of the following statements is analogous to 'an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force'?

A) A rotating body continues to rotate with the same angular velocity unless acted upon by a net torque. B) A stationary body remains stationary unless acted upon by a torque. C) A rotating body stops rotating unless acted upon by a torque. D) A body's moment of inertia changes with its angular velocity.

30. If a constant torque is applied to a rigid body, its angular acceleration will be:

A) Variable B) Constant C) Zero D) Dependent on angular velocity

31. The relationship between angular displacement (θ) and the arc length (s) subtended at the circumference of a circle of radius r is:

A) s = θ/r B) s = r/θ C) s = rθ D) s = r^2 θ

32. Which equation describes the change in angular momentum (ΔL) due to an applied torque (τ) over a time interval (Δt)?

A) ΔL = τ / Δt B) ΔL = τ * Δt C) ΔL = τ + Δt D) ΔL = τ - Δt

33. If the linear velocity of a point on a rotating object is doubled, what happens to its angular velocity, assuming the radius remains constant?

A) It is halved B) It is doubled C) It remains the same D) It increases by a factor of four

34. The rotational analogue of momentum conservation (if net force is zero, momentum is conserved) is:

A) Conservation of angular momentum (if net torque is zero, angular momentum is conserved). B) Conservation of moment of inertia (if net torque is zero, moment of inertia is conserved). C) Conservation of angular acceleration (if net torque is zero, angular acceleration is conserved). D) Conservation of angular velocity (if net torque is zero, angular velocity is conserved).

35. Which equation relates the final angular velocity (ω_f), initial angular velocity (ω_i), angular acceleration (α), and angular displacement (θ) without involving time?

A) ω_f = ω_i + αt B) θ = ω_i t + 1/2 αt^2 C) ω_f^2 = ω_i^2 + 2αθ D) τ = Iα

36. If a net torque of zero acts on a rigid body, the body will have:

A) Zero angular acceleration B) Zero angular velocity C) Constant angular velocity D) Both (a) and (c)

37. Which of the following is a scalar quantity?

A) Angular velocity B) Angular acceleration C) Angular displacement D) Torque

38. Which of the following is a vector quantity?

A) Moment of inertia B) Angular velocity C) Angular kinetic energy D) Work done in rotation

39. The magnitude of angular momentum of a rigid body rotating about a fixed axis is given by:

A) I / ω B) I * α C) I * ω D) I + ω

40. If a body is initially at rest and a constant torque is applied, its angular displacement is proportional to:

A) t B) t^2 C) t^3 D) sqrt(t)

41. The rotational analogue of potential energy is not directly defined in the same way as linear motion, but changes in angular position can be related to potential energy in specific contexts like gravity for extended bodies.

A) True B) False C) Sometimes true D) Only for point masses

42. Which equation correctly shows the relationship between torque (τ), moment of inertia (I), and angular acceleration (α) for a rigid body?

A) τ = I / α B) τ = α / I C) τ = I * α D) τ = I + α

43. If a body is rotating with constant angular acceleration, its angular velocity changes:

A) Linearly with time B) Quadratically with time C) Inversely with time D) Not at all

44. The comparison between linear and rotational motion equations is valid under which condition?

A) Only for translational motion B) Only for rotational motion C) When the body is rigid and the acceleration is constant D) Always valid regardless of motion type

45. The rotational analogue of mass (m) is moment of inertia (I). This analogy holds because both quantities resist changes in motion.

A) True B) False C) Partially true D) Depends on the type of motion

46. Which equation directly relates the change in angular velocity (Δω) to the angular impulse (τΔt) and moment of inertia (I)?

A) Δω = (τΔt) / I B) Δω = I / (τΔt) C) Δω = (τΔt) * I D) Δω = I + (τΔt)

47. If the angular displacement is plotted against time for a body undergoing constant angular acceleration starting from rest, the graph will be a:

A) Straight line B) Parabola C) Hyperbola D) Circle

48. The relationship between angular frequency (ω) in SHM and angular velocity in uniform circular motion is that they are numerically equal, but angular velocity is a vector.

A) True B) False C) Sometimes true D) Only if the motion is simple harmonic

49. In the context of rotational motion, what does 'rigid body' imply?

A) The body is unbreakable B) The distance between any two particles in the body remains constant C) The body has zero mass D) The body is at rest

50. Which equation implies that if a body is rotating, it will continue to do so with the same angular velocity unless acted upon by an external torque?

A) τ = Iα B) L = Iω C) If τ_net = 0, then α = 0 D) ω_f = ω_i + αt

Equations of rotational motion and comparison with linear motion - Online Test

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