What is the product of the moment of inertia and angular acceleration?

• A. Energy
• B. Torque
• C. Momentum
• D. Force

Answer: (B)

Torque is the product of the moment of inertia and angular acceleration because it is the rotational analogue of force. For a rigid body rotating about a fixed axis with constant I, the net torque τ causes the angular speed to change according to τ = I α. This comes from the relation between angular momentum L = I ω and its rate of change: dL/dt = I α, so the torque that produces that change is equal to I α. The units line up as well: kg·m^2 times rad/s^2 gives N·m, the unit of torque. In contrast, energy depends on ω as 1/2 I ω^2, angular momentum is I ω, and force relates to linear acceleration, not angular acceleration. So the product I α uniquely identifies torque.