Moment of Inertia, Angular Momentum and Rotational Motion - One Line Questions

1. What is the moment of inertia of a thin uniform ring of mass M and radius R about an axis passing through its center and perpendicular to its plane? — MR^2
2. The moment of inertia of a cone of mass M and radius R about its central axis is: — 2/5 MR^2
3. Rotational kinetic energy of a body is given by: — 1/2 Iω^2
4. If the angular velocity of a rotating body is doubled, its rotational kinetic energy changes by a factor of: — 4
5. The relationship between linear acceleration (a) and angular acceleration (α) for a point on a rotating body at radius 'r' is: — a = αr
6. For a given mass distribution and shape, which axis of rotation will result in the smallest moment of inertia? — An axis passing through the center of mass
7. Which quantity is conserved in the absence of external torque? — Angular momentum
8. The gyroscopic effect, observed in spinning tops and gyroscopes, is a direct consequence of: — Conservation of angular momentum
9. An ice skater spins faster when she pulls her arms in. This is an example of the principle of: — Conservation of angular momentum
10. When a body rotates, its total kinetic energy is the sum of its translational and rotational kinetic energies. This is known as: — Combined motion
11. A planet orbits the Sun. If the planet's orbit is an ellipse, its angular momentum about the Sun is: — Constant
12. If a body's mass is concentrated closer to the axis of rotation, its moment of inertia will be: — Lower
13. The Parallel Axis Theorem relates the moment of inertia about an axis through the center of mass to the moment of inertia about a parallel axis at a distance 'd'. The theorem states: — I = I_cm + Md^2
14. For a rigid body, the moment of inertia is the sum of the moments of inertia of its constituent particles. Mathematically, it is represented as: — I = Σ m_i r_i^2
15. The Perpendicular Axis Theorem states that for a planar body, the moment of inertia about an axis perpendicular to the plane is the sum of the moments of inertia about two axes in the plane that are perpendicular to each other at the point where the first axis passes through. Mathematically: — I_z = I_x + I_y
16. A child sits on a merry-go-round that is rotating at a constant speed. If the child moves from the edge towards the center, the angular velocity of the merry-go-round will: — Remain the same
17. In the equation L = Iω, if I decreases, ω must: — Increase to conserve L
18. If a body is in equilibrium, what can be said about the net torque acting on it? — It is zero
19. Which factor significantly influences the moment of inertia of a body? — The distribution of its mass relative to the axis of rotation
20. The SI unit of angular momentum is: — kg m^2/s
21. What is the unit of moment of inertia in the SI system? — kg m^2
22. For a rigid body rotating with angular velocity ω about a fixed axis, its angular momentum is given by: — L = Iω
23. A thin rod of mass M and length L is rotated about an axis passing through its center and perpendicular to its length. What is its moment of inertia? — ML^2/12
24. What is the moment of inertia of a thin rod of mass M and length L about an axis passing through one of its ends and perpendicular to its length? — ML^2/3
25. Which of the following quantities is a vector? — Angular Velocity
26. The rotational equivalent of force is: — Torque
27. The moment of inertia of a point mass 'm' at a distance 'r' from the axis of rotation is given by: — mr^2
28. The moment of inertia of a solid cylinder of mass M and radius R about its central axis is: — 1/2 MR^2
29. The moment of inertia of a hollow cylinder (thin walled) of mass M and radius R about its central axis is: — MR^2
30. What is the moment of inertia of a solid sphere of mass M and radius R about an axis passing through its center? — 2/5 MR^2
31. The moment of inertia of a hollow sphere (thin walled) of mass M and radius R about an axis passing through its center is: — 2/3 MR^2
32. The moment of inertia of a circular disk of mass M and radius R about an axis passing through its center and perpendicular to its plane is: — 1/2 MR^2
33. Which of the following is NOT a unit of torque? — Joule
34. The SI unit of torque is: — Newton-meter (N m)
35. Which theorem is useful for calculating the moment of inertia of a body about an axis that does not pass through its center of mass? — Parallel Axis Theorem
36. Angular momentum (L) of a particle of mass 'm' moving with velocity 'v' at position 'r' relative to the origin is defined as: — r x p
37. If a net external torque acts on a system, its angular momentum will: — Change according to the net torque
38. The moment of inertia of a body depends on its: — All of the above
39. The moment of inertia of a system of particles about an axis is independent of: — The total kinetic energy of the system
40. What is the definition of moment of inertia? — The resistance of a rotating body to changes in its state of angular motion.
41. A sphere and a disk of the same mass and radius roll down an inclined plane without slipping. Which will reach the bottom first? — The sphere
42. The law of conservation of angular momentum states that if the net external torque acting on a system is zero, then: — The total angular momentum of the system is constant.
43. The rotational equivalent of mass is: — Moment of inertia
44. For rolling motion without slipping, the condition relating linear velocity (v) and angular velocity (ω) for a body of radius R is: — v = ωR
45. A particle moves in a circle of radius 'r' with constant speed 'v'. Its angular velocity is: — v/r
46. A rigid body is rotating with constant angular velocity. This implies that the net external torque on the body is: — Zero
47. Angular acceleration (α) is the rate of change of angular velocity. Mathematically: — α = dω/dt
48. The moment of inertia of a diatomic molecule about an axis passing through its center of mass and perpendicular to the bond is approximately: — μd^2
49. Torque (τ) is the rotational analog of force. It is defined as the rate of change of angular momentum. Mathematically: — τ = dL/dt
50. Torque is also defined as the cross product of the position vector 'r' and the force vector 'F'. Mathematically: — τ = r x F
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