Which quantity represents the resistance to changes in rotational motion?

• A. Speed
• B. Mass
• C. Moment of Inertia
• D. Torque

Answer: (C)

Moment of inertia measures how hard it is to change an object's rotational motion. It plays the same role for rotation that mass does for linear motion: a larger inertia means a larger resistance to speeding up or slowing down when a torque is applied. This shows up in the rotational version of Newton’s second law, where torque equals the moment of inertia times angular acceleration (τ = Iα). Because I depends on how mass is distributed relative to the axis (I = ∑ m r^2 or ∫ r^2 dm), mass that sits farther from the axis increases the resistance to changes in rotation. So, even if you apply the same torque, an object with a larger moment of inertia will have a smaller angular acceleration, making it harder to change its rotational state. Speed is simply how fast something is rotating right now, not how hard it is to change that rotation, and torque is what you apply to try to cause the change. That connection to Newton’s second law for rotation is why moment of inertia is the correct quantity.