Moment of a force, torque, angular momentum, conservation of angular momentum and applications - Question Bank

1. For a rigid body rotating about a fixed axis, the net external torque is equal to the product of:
A) Its moment of inertia and its angular acceleration
B) Its mass and its angular velocity
C) Its radius and its angular momentum
D) Its angular velocity and its angular acceleration
2. A boy is standing on a rotating platform holding weights. If he extends his arms outwards, his angular velocity will:
A) Decrease
B) Increase
C) Remain the same
D) Become zero
3. The change in angular momentum of a body is directly proportional to the applied:
A) Torque and the time interval
B) Force and the time interval
C) Moment of inertia and angular velocity
D) Angular acceleration and angular velocity
4. A particle moves in a circle of radius r with constant speed v. Its angular momentum about the center of the circle is:
A) mvr
B) mv/r
C) mr/v
D) Zero
5. Which of the following is a unit of torque?
A) Newton-meter
B) Joule
C) Watt
D) Pascal
6. If a force vector and the position vector are collinear, the torque produced is:
A) Zero
B) Maximum
C) Infinite
D) Equal to the force
7. The moment of inertia of a hollow sphere of mass M and radius R about an axis through its center is:
A) ²⁄₃MR²
B) MR²
C) ½MR²
D) ML²
8. What is the condition for rotational equilibrium?
A) Sum of clockwise torques = Sum of anticlockwise torques
B) Sum of clockwise torques > Sum of anticlockwise torques
C) Sum of clockwise torques < Sum of anticlockwise torques
D) Torque is maximum
9. A force is applied at the center of a wheel. The torque produced about the center is:
A) Zero
B) Maximum
C) Dependent on angular velocity
D) Dependent on moment of inertia
10. The angular momentum of a particle of mass m with position vector r and velocity v is given by:
A) m(r × v)
B) m(v × r)
C) m(r · v)
D) m(r + v)
11. A flywheel is spinning at a constant rate. This implies:
A) The net torque on the flywheel is zero
B) The moment of inertia is zero
C) The angular momentum is zero
D) The angular acceleration is non-zero
12. Which of the following statements is true about angular momentum?
A) It is conserved in the absence of external torque.
B) It is always zero for a moving particle.
C) Its direction is always along the velocity vector.
D) It is a scalar quantity.
13. A particle is projected with velocity v. What is the torque of gravity about the point of projection?
A) Zero
B) Non-zero and constant
C) Increases with time
D) Decreases with time
14. If the distance of the force from the axis of rotation is doubled, the torque:
A) Is doubled
B) Is halved
C) Remains the same
D) Becomes zero
15. The moment of inertia of a solid sphere of mass M and radius R about an axis through its center is:
A) ²⁄₅MR²
B) MR²
C) ½MR²
D) ML²
16. A system is in equilibrium if:
A) Net force and net torque are both zero
B) Net force is zero and net torque is non-zero
C) Net force is non-zero and net torque is zero
D) Net force and net torque are both non-zero
17. What is the angular momentum of a particle of mass m moving with velocity v at a position r from the origin if r and v are perpendicular?
A) mvr
B) mv/r
C) mr/v
D) Zero
18. Torque is a vector quantity. Its direction is determined by:
A) The right-hand rule
B) The left-hand rule
C) The direction of the force
D) The direction of the lever arm
19. When a dancer pulls their legs and arms inwards, their angular speed increases. This is a direct consequence of:
A) Conservation of angular momentum
B) Conservation of linear momentum
C) Conservation of kinetic energy
D) Change in mass
20. A satellite in an elliptical orbit around the Earth has its angular momentum conserved because:
A) The gravitational force is a central force
B) The satellite's speed is constant
C) The distance from the Earth is constant
D) There is no atmosphere in space
21. The moment of inertia of a thin ring of mass M and radius R about an axis through its center and perpendicular to its plane is:
A) MR²
B) ½MR²
C) ²⁄₃MR²
D) ML²
22. If a body has zero net torque, its angular momentum:
A) Remains constant
B) Becomes zero
C) Increases linearly with time
D) Decreases linearly with time
23. A force of 5 N is applied at a distance of 20 cm from the pivot. What is the torque if the force is applied at an angle of 30 degrees to the lever arm?
A) 0.5 N·m
B) 1 N·m
C) 0.866 N·m
D) 2 N·m
24. The rate of change of angular momentum of a particle is equal to:
A) The net external torque acting on it
B) The net external force acting on it
C) The moment of inertia
D) The angular velocity
25. When a spinning top is on the verge of falling, its axis of rotation starts to wobble. This phenomenon is known as:
A) Precession
B) Nutation
C) Gyroscopic effect
D) Resonance
26. A uniform rod of mass M and length L is rotating about its center. If a force is applied at one end perpendicular to the rod, it produces:
A) Angular acceleration
B) Linear acceleration
C) Constant angular velocity
D) Constant angular momentum
27. The torque required to change the angular momentum of a system from L1 to L2 in time t is:
A) (L2 - L1) / t
B) (L1 - L2) / t
C) L1 * t / L2
D) L2 * t / L1
28. A particle of mass 2 kg is moving with a velocity of 3 m/s along the x-axis at y = 4 m. What is its angular momentum about the origin?
A) 24 kg·m²/s (in the +z direction)
B) 18 kg·m²/s (in the +z direction)
C) 12 kg·m²/s (in the -z direction)
D) Zero
29. Which quantity is the rotational analogue of linear momentum?
A) Angular momentum
B) Moment of inertia
C) Torque
D) Angular velocity
30. Which quantity is the rotational analogue of force?
A) Torque
B) Moment of inertia
C) Angular momentum
D) Angular acceleration
31. Which quantity is the rotational analogue of mass?
A) Moment of inertia
B) Torque
C) Angular momentum
D) Angular velocity
32. A particle is moving in a straight line with constant speed. Its angular momentum about any point on the line of motion is:
A) Zero
B) Constant and non-zero
C) Increasing
D) Decreasing
33. If a body is rotating with constant angular velocity, what is the net external torque acting on it?
A) Zero
B) Non-zero but constant
C) Variable
D) Equal to its angular momentum
34. A force F acts at point P. The torque about a point O is given by:
A) r x F (where r is the vector from O to P)
B) F x r (where r is the vector from O to P)
C) r * F (where r is the distance from O to P)
D) F / r (where r is the distance from O to P)
35. The moment of inertia of a rigid body depends on:
A) Mass distribution and the axis of rotation
B) Total mass only
C) Angular velocity only
D) Applied torque only
36. If the angular momentum of a system is L and it changes to L' in time Δt, the average external torque is given by:
A) (L' - L) / Δt
B) L' * Δt
C) L / Δt
D) (L + L') / Δt
37. What is the direction of the torque vector for a force applied tangentially to a circle of radius r?
A) Perpendicular to the plane of rotation
B) Along the radius
C) Along the tangent
D) Opposite to the force
38. When a diver tucks their body during a somersault, their angular velocity increases. This is due to:
A) Decrease in their moment of inertia
B) Increase in their moment of inertia
C) Constant moment of inertia
D) External torque
39. A planet revolves around the Sun. If the gravitational force between them is considered, is angular momentum conserved?
A) Yes, because the gravitational force is a central force and produces no torque about the Sun
B) No, because the planet is in motion
C) Yes, because the planet has mass
D) No, because the Sun has mass
40. For a system of particles, the total angular momentum is the:
A) Vector sum of the angular momenta of individual particles
B) Scalar sum of the angular momenta of individual particles
C) Average of the angular momenta of individual particles
D) Product of the angular momenta of individual particles
41. The moment of inertia of a point mass m at a distance r from the axis of rotation is given by:
A) mr²
B) mvr
C) mr
D) mv²/r
42. Which of the following is a vector quantity?
A) Torque
B) Moment of inertia
C) Mass
D) Angular velocity magnitude
43. A particle of mass m moves with a constant velocity v. Its angular momentum about the origin is:
A) Constant if the velocity vector passes through the origin
B) Always zero
C) Constant regardless of the origin's position
D) Zero only if the particle is at rest
44. If a rigid body is rotating about a fixed axis, the torque is related to its angular acceleration by:
A) τ = Iα (where I is moment of inertia and α is angular acceleration)
B) τ = L/t (where L is angular momentum and t is time)
C) τ = Fd (where F is force and d is distance)
D) τ = mvr (where m is mass, v is velocity, and r is radius)
45. An ice skater spins faster when she pulls her arms closer to her body. This is an example of:
A) Conservation of angular momentum
B) Conservation of linear momentum
C) Conservation of energy
D) Newton's first law of motion
46. The law of conservation of angular momentum states that if the net external torque acting on a system is zero, then:
A) The total angular momentum of the system remains constant
B) The total linear momentum of the system remains constant
C) The total kinetic energy of the system remains constant
D) The total potential energy of the system remains constant
47. What is the SI unit of angular momentum?
A) Joule-second (J·s)
B) Newton-meter (N·m)
C) Kilogram-meter²/second (kg·m²/s)
D) Radian/second (rad/s)
48. Angular momentum of a particle is given by:
A) r x p (where r is position vector and p is linear momentum)
B) r x v (where r is position vector and v is velocity)
C) m x v (where m is mass and v is velocity)
D) I x ω (where I is moment of inertia and ω is angular velocity)
49. If a force of 10 N is applied at a perpendicular distance of 0.5 m from the pivot of a lever, what is the torque produced?
A) 2 N·m
B) 5 N·m
C) 10 N·m
D) 20 N·m
50. Torque is defined as the product of:
A) Force and perpendicular distance from the axis of rotation
B) Mass and velocity
C) Force and velocity
D) Mass and acceleration
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