TORQUE ANGULAR
MOMENTUM AND EQUILIBRIUM
1. Torque is defined as the cross product of force and:
- a) Displacement
- b) Velocity
- c) Acceleration
- d) Momentum
2. The SI unit of torque is:
- a) Newton-meter (N⋅m)
- b) Kilogram-meter (kg⋅m)
- c) Joule (J)
- d) Watt (W)
3. The moment arm is the perpendicular distance between the:
- a) Force and the axis of rotation
- b) Velocity and the axis of rotation
- c) Acceleration and the axis of rotation
- d) Torque and the axis of rotation
4. Which of the following factors affects torque?
- a) Force and distance
- b) Velocity and time
- c) Mass and acceleration
- d) Power and energy
5. Angular momentum depends on the object's:
- a) Mass and acceleration
- b) Mass and velocity
- c) Mass and displacement
- d) Mass and moment of inertia
6. Angular momentum is a vector quantity with direction:
- a) Parallel to the force applied
- b) Parallel to the angular velocity
- c) Perpendicular to the plane of rotation
- d) Opposite to the direction of motion
7. According to the conservation of angular momentum, angular momentum is conserved when:
- a) No external torques act on a system
- b) No internal torques act on a system
- c) The moment arm is zero
- d) The object's mass is constant
8. Which of the following objects has the highest rotational inertia?
- a) A thin rod
- b) A thick rod
- c) A small sphere
- d) A large sphere
9. Equilibrium occurs when the net force and net torque on an object are:
- a) Both zero
- b) Non-zero
- c) Opposite in direction
- d) Equal in magnitude
10. The condition for translational equilibrium is:
- a) Net force is zero
- b) Net torque is zero
- c) Both net force and net torque are zero
- d) Both net force and net torque are non-zero
11. A system is in rotational equilibrium if the sum of all torques acting on it is:
- a) Zero
- b) Non-zero
- c) Positive
- d) Negative
12. The center of mass of an object:
- a) Always coincides with the geometric center
- b) Is located at the axis of rotation
- c) Depends on the shape and mass distribution of the object
- d) Remains fixed regardless of external forces
13. Which of the following statements about equilibrium is correct?
- a) An object in equilibrium must be at rest
- b) An object in equilibrium can have zero net force but non-zero net torque
- c) An object in equilibrium can have zero net torque but non-zero net force
- d) An object in equilibrium cannot have any external forces acting on it
14. The rotational inertia depends on:
- a) Mass and acceleration
- b) Force and distance
- c) Shape and mass distribution
- d) Velocity and time
15. The conservation of angular momentum is analogous to:
- a) Conservation of linear momentum
- b) Conservation of energy
- c) Conservation of charge
- d) Conservation of mass
16. If the moment arm is increased, while keeping the force constant, the torque will:
- a) Increase
- b) Decrease
- c) Remain the same
- d) Become negative
17. Which of the following is an example of static equilibrium?
- a) A car moving at a constant velocity
- b) A person sitting on a chair
- c) A swinging pendulum
- d) A rocket taking off
18. The center of mass of a symmetrical object lies:
- a) Inside the object
- b) Outside the object
- c) At the geometric center
- d) None of the above
19. An object in rotational equilibrium means that:
- a) The object is not rotating
- b) The object is rotating at a constant speed
- c) The object's angular momentum is constant
- d) The object experiences no net torque
20. The condition for rotational equilibrium is:
- a) Net force is zero
- b) Net torque is zero
- c) Both net force and net torque are zero
- d) Both net force and net torque are non-zero
21. The moment of inertia depends on:
- a) Mass and acceleration
- b) Force and distance
- c) Shape and mass distribution
- d) Velocity and time
22. Which of the following statements is true about the center of mass of a system of particles?
- a) It is always located at the geometric center
- b) It is the point where the net force acts
- c) It remains fixed regardless of external forces
- d) It is calculated by dividing the total mass by the total volume
23. Which of the following objects has the highest rotational inertia?
- a) A thin disk
- b) A thick disk
- c) A small sphere
- d) A large sphere
24. The angular momentum of a rotating object depends on:
- a) Its mass and velocity
- b) Its mass and acceleration
- c) Its force and displacement
- d) Its torque and time
25. A system is in translational equilibrium if:
- a) The net force acting on it is zero
- b) The net torque acting on it is zero
- c) Both the net force and net torque are zero
- d) The system is at rest
26. If an object's center of mass is outside the object, the object will:
- a) Not be in equilibrium
- b) Have a net force acting on it
- c) Have a non-zero net torque
- d) Have zero angular momentum
27. The torque exerted by a force is maximum when the angle between the force and the moment arm is:
- a) 0 degrees
- b) 45 degrees
- c) 90 degrees
- d) 180 degrees
28. The principle of conservation of angular momentum states that angular momentum is conserved:
- a) Only when no external torques act on a system
- b) Only when no internal torques act on a system
- c) Only when no net forces act on a system
- d) When no external or internal torques act on a system
29. Which of the following objects has the highest moment of inertia about its central axis?
- a) A solid cylinder
- b) A hollow cylinder
- c) A solid sphere
- d) A hollow sphere
30. The center of mass of an irregularly shaped object:
- a) Always coincides with the geometric center
- b) Is located at the axis of rotation
- c) Depends on the shape and mass distribution of the object
- d) Remains fixed regardless of external forces
31. An object will topple over when the line of action of its weight falls:
- a) Inside its base of support
- b) Outside its base of support
- c) At its center of mass
- d) Along its axis of rotation
32. The angular velocity of an object in rotational motion depends on:
- a) The net force acting on the object
- b) The mass of the object
- c) The moment of inertia of the object
- d) The linear velocity of the object
33. Which of the following statements about equilibrium is correct?
- a) An object in equilibrium must be at rest
- b) An object in equilibrium can have zero net force but non-zero net torque
- c) An object in equilibrium can have zero net torque but non-zero net force
- d) An object in equilibrium cannot have any external forces acting on it
34. The principle of conservation of angular momentum applies to:
- a) Rotational motion only
- b) Translational motion only
- c) Both rotational and translational motion
- d) None of the above
35. A system is in rotational equilibrium if the sum of all torques acting on it is:
- a) Zero
- b) Non-zero
- c) Positive
- d) Negative
36. Which of the following objects has the lowest rotational inertia?
- a) A thin rod
- b) A thick rod
- c) A small sphere
- d) A large sphere
37. The center of mass of a symmetrical object lies:
- a) Inside the object
- b) Outside the object
- c) At the geometric center
- d) None of the above
38. The torque exerted by a force depends on:
- a) The magnitude of the force and the distance from the axis of rotation
- b) The mass of the object and its angular velocity
- c) The direction of the force and the moment of inertia
- d) The velocity of the object and the time of application
39. The moment arm is the perpendicular distance between the:
- a) Force and the axis of rotation
- b) Velocity and the axis of rotation
- c) Acceleration and the axis of rotation
- d) Torque and the axis of rotation
40. An object will be in translational equilibrium if the sum of the forces acting on it is:
- a) Zero
- b) Non-zero
- c) Equal to its weight
- d) Equal to its momentum
ANSWER KEY:
- b) Velocity
- a) Newton-meter (N⋅m)
- a) Force and the axis of rotation
- a) Force and distance
- d) Mass and moment of inertia
- c) Perpendicular to the plane of rotation
- a) No external torques act on a system
- d) A large sphere
- a) Both zero
- b) Net torque is zero
- a) Zero
- c) Depends on the shape and mass distribution of the object
- c) An object in equilibrium can have zero net torque but non-zero net force
- c) Shape and mass distribution
- a) Conservation of linear momentum
- a) Increase
- b) A person sitting on a chair
- c) At the geometric center
- d) The object experiences no net torque
- b) Net torque is zero
- c) Shape and mass distribution
- c) It remains fixed regardless of external forces
- b) A thick rod
- a) Its mass and velocity
- a) The net force acting on it is zero
- a) Not be in equilibrium
- c) 90 degrees
- a) Only when no external torques act on a system
- b) A hollow cylinder
- c) Depends on the shape and mass distribution of the object
- b) Outside its base of support
- c) The moment of inertia of the object
- b) An object in equilibrium can have zero net force but non-zero net torque
- c) Both rotational and translational motion
- a) Zero
- a) A thin rod
- c) At the geometric center
- a) The magnitude of the force and the distance from the axis of rotation
- a) Force and the axis of rotation
- a) Zero
