The rotational counterpart to force is known as what?

• A. Angular Momentum
• B. Moment of Inertia
• C. Radius of Gyration
• D. Torque

Answer: (D)

Torque is the turning effect of a force. When a force is applied at some distance from an axis, it tends to spin the object rather than just push it straight. This turning influence is described by the torque, τ, which equals the lever arm times the force in the appropriate direction: τ = r × F, with magnitude τ = r F sinθ. The direction of τ follows the right-hand rule.

Torque is what changes rotational motion in the same way force changes linear motion. For a rigid body rotating about a fixed axis, the angular acceleration α is produced by torque through τ = I α, where I is the moment of inertia, a measure of how hard it is to spin the object. This parallels F = m a in linear motion, with angular equivalents: torque plays the role of force, angular acceleration the role of linear acceleration, and moment of inertia the role of mass.

Angular momentum, L = I ω, is the quantity that changes when torque acts. The moment of inertia is a property that resists changes in rotation, and the radius of gyration is just a way to express I as Mk^2. So the turning action produced by a force at a distance is best described by torque.