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

1. The angular momentum of a particle about a point O is given by L = r × p. If the particle moves such that its velocity vector is always parallel to the position vector, its angular momentum about O will be:
A) Zero
B) Constant and non-zero
C) Increasing
D) Decreasing
2. A force F = (2i + 3j) N acts at a point r = (4i + 2j) m. The torque about the origin is:
A) -8k N m
B) 8k N m
C) 14k N m
D) -14k N m
3. When the net torque on a system is zero, the quantity that remains constant is:
A) Angular momentum
B) Angular velocity
C) Moment of inertia
D) Rotational kinetic energy
4. For a particle moving in a circle of radius R with speed v, its angular momentum about the center of the circle is proportional to:
A) v
B) R^2
C) 1/v
D) 1/R
5. Which of the following is NOT a unit of torque?
A) Newton-meter
B) Joule
C) Dyne-centimeter
D) Pound-foot
6. The direction of angular momentum vector is typically taken along the:
A) Axis of rotation
B) Direction of linear velocity
C) Direction of applied force
D) Direction of moment of inertia
7. If the position vector of a particle is r and its linear momentum is p, its angular momentum L is given by:
A) r × p
B) p × r
C) r ⋅ p
D) p ⋅ r
8. A force of 10 N is applied tangentially to a wheel of radius 0.5 m. The torque produced is:
A) 5 N m
B) 20 N m
C) 0.5 N m
D) 10 N m
9. If the angular momentum of a system changes, it means that:
A) A net external torque is acting on the system
B) A net external force is acting on the system
C) The moment of inertia is changing
D) The angular velocity is constant
10. The angular momentum of a particle is zero if:
A) The particle is at rest
B) The particle moves along a line passing through the origin
C) The particle's velocity is zero
D) All of the above
11. A force F acts at a distance r from a pivot. The torque is maximum when the angle between F and r is:
A) 90 degrees
B) 0 degrees
C) 180 degrees
D) 45 degrees
12. Which quantity is conserved in a system upon which no external torque acts?
A) Angular momentum
B) Linear momentum
C) Total energy
D) Moment of inertia
13. If a body is rotating with angular velocity ω and has moment of inertia I, its rotational kinetic energy is given by:
A) 1/2 I ω^2
B) I ω
C) 1/2 I ω
D) I ω^2
14. A particle of mass 2 kg is moving with a velocity of (3i + 4j) m/s. Its angular momentum about the origin is:
A) k (24i - 18j) kg m^2/s
B) k (18i - 24j) kg m^2/s
C) k (24i + 18j) kg m^2/s
D) k (18i + 24j) kg m^2/s
15. The angular momentum of a particle about the origin is L. If the particle moves to a new position such that its position vector is doubled, while its momentum remains the same, the new angular momentum will be:
A) 2L
B) 4L
C) L/2
D) L
16. What is the angular momentum of a particle of mass m moving with velocity v in a straight line, about a point P on the line of motion?
A) Zero
B) mv
C) mvr
D) Infinite
17. The moment of a couple is equal to the product of the magnitude of one force and the:
A) Perpendicular distance between the lines of action of the two forces
B) Sum of the two forces
C) Distance from the pivot to the point of application of the force
D) Square of the distance between the forces
18. A couple consists of two forces which are:
A) Equal in magnitude, opposite in direction, and acting along different lines
B) Equal in magnitude, opposite in direction, and acting along the same line
C) Unequal in magnitude, opposite in direction, and acting along different lines
D) Equal in magnitude, same direction, and acting along different lines
19. If the moment of inertia of a rotating body is halved, and its angular momentum remains constant, its angular velocity will:
A) Double
B) Halve
C) Remain the same
D) Become zero
20. The angular momentum of a particle is conserved if:
A) The net external torque acting on it is zero
B) The net external force acting on it is zero
C) Its velocity is constant
D) Its kinetic energy is constant
21. A force of 5 N acts on a position vector of (3i + 4j) m. The torque produced about the origin is:
A) 15 k N m
B) 20 k N m
C) -15 k N m
D) -20 k N m
22. A particle of mass m is projected with velocity v at an angle θ with the horizontal. What is its angular momentum about the point of projection when it reaches the highest point of its trajectory?
A) Zero
B) m(v cos θ) H, where H is the horizontal range
C) m(v sin θ) h, where h is the maximum height
D) mvH
23. If a force F acts at a distance r, and the angle between r and F is θ, the magnitude of torque is given by:
A) rF sin(θ)
B) rF cos(θ)
C) rF tan(θ)
D) rF
24. When a body is subjected to a torque, its angular momentum changes at a rate equal to:
A) The applied torque
B) The angular velocity
C) The moment of inertia
D) The kinetic energy
25. A rigid body is rotating with constant angular velocity. This implies that:
A) The net torque acting on it is zero
B) The net force acting on it is zero
C) Its moment of inertia is zero
D) Its angular momentum is zero
26. The angular momentum of a particle about a point O is zero if:
A) The particle is at O
B) The particle moves directly towards or away from O
C) The particle moves in a circle centered at O
D) All of the above
27. A particle is rotating 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) mvr^2
28. Which of the following statements about angular momentum is correct?
A) It is the product of moment of inertia and angular velocity.
B) It is the product of force and time.
C) It is the product of mass and velocity.
D) It is the product of torque and time.
29. If a force F is applied at a distance r, and F is perpendicular to r, the magnitude of torque is:
A) Fr
B) F/r
C) r/F
D) F+r
30. What is the direction of torque when a force is applied to rotate an object counter-clockwise?
A) Perpendicular to the plane of rotation, out of the plane
B) Perpendicular to the plane of rotation, into the plane
C) Along the axis of rotation
D) In the plane of rotation
31. If the net torque on a system is zero, then the angular momentum of the system:
A) Is conserved
B) Is zero
C) Increases linearly with time
D) Decreases linearly with time
32. A spinning ice skater pulls her arms in to decrease her moment of inertia. According to the conservation of angular momentum, her angular velocity will:
A) Increase
B) Decrease
C) Remain the same
D) Become zero
33. The conservation of angular momentum is a consequence of which law of physics?
A) Newton's third law
B) Newton's first law
C) Newton's second law
D) Law of conservation of energy
34. Angular momentum is related to the rotational inertia and:
A) Angular velocity
B) Angular acceleration
C) Linear velocity
D) Linear acceleration
35. If a force is applied along the line passing through the pivot, the torque produced is:
A) Zero
B) Maximum
C) Negative
D) Infinite
36. What happens to the torque if the perpendicular distance from the pivot to the line of action of the force is doubled?
A) It doubles
B) It halves
C) It quadruples
D) It remains the same
37. Which of the following is a unit of torque?
A) Newton-meter
B) Joule
C) Watt
D) Pascal
38. A force of 10 N acts at a point P which is 2 m away from a pivot O. If the angle between the force vector and the position vector OP is 30 degrees, what is the magnitude of the torque?
A) 10 N m
B) 20 N m
C) 5 N m
D) 17.32 N m
39. A force of 10 N is applied at a distance of 5 m from the pivot. What is the magnitude of the torque if the force is perpendicular to the lever arm?
A) 50 N m
B) 15 N m
C) 5 N m
D) 2 N m
40. If no external torque acts on a system of particles, which quantity is conserved?
A) Angular momentum
B) Linear momentum
C) Kinetic energy
D) Moment of inertia
41. The rate of change of angular momentum of a particle is equal to:
A) The net torque acting on the particle
B) The net force acting on the particle
C) The angular velocity
D) The linear momentum
42. For a particle of mass m moving with velocity v at a position vector r from the origin, the angular momentum L is given by:
A) r × (mv)
B) mv × r
C) r × v
D) v × r
43. The SI unit of angular momentum is:
A) Joule-second (J s)
B) Newton-meter (N m)
C) Kilogram-meter per second (kg m/s)
D) Radian per second (rad/s)
44. Angular momentum of a particle is defined as the product of:
A) Position vector and linear momentum
B) Velocity vector and mass
C) Force and time
D) Acceleration and time
45. What is the condition for a rigid body to be in rotational equilibrium?
A) Net torque acting on the body is zero
B) Net force acting on the body is zero
C) Net angular momentum is conserved
D) Net kinetic energy is zero
46. Torque is the rotational analogue of which linear quantity?
A) Force
B) Momentum
C) Velocity
D) Acceleration
47. If a force F acts at a position vector r from the pivot, the torque is given by:
A) r × F
B) F × r
C) r ⋅ F
D) F ⋅ r
48. Which of the following quantities is a vector quantity?
A) Moment of a force
B) Mass
C) Speed
D) Distance
49. The moment of a force is defined as the product of:
A) Force and perpendicular distance from the pivot to the line of action of the force
B) Force and distance along the line of action of the force
C) Mass and velocity
D) Mass and acceleration
50. What is the SI unit of the moment of a force (torque)?
A) Newton-meter (N m)
B) Joule (J)
C) Newton (N)
D) Pascal (Pa)
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