Which description correctly defines the moment of inertia?

• A. A rate of change of angular velocity.
• B. A mass property that determines the torque needed for a given angular acceleration.
• C. The total force acting on the object.
• D. The distance from the axis of rotation.

Answer: (B)

Moment of inertia is the measure of an object's resistance to changes in its rotational motion. It depends on how mass is distributed relative to the axis of rotation, because mass farther from the axis contributes more to resisting spin. The precise relationship to torque and angular acceleration is given by τ = I α, where torque equals the moment of inertia times the angular acceleration. This means that for a given angular acceleration, a larger moment of inertia requires a larger torque to achieve that acceleration. That is why the description “a mass property that determines the torque needed for a given angular acceleration” best captures the concept.

To clarify the distinctions: angular velocity and its rate of change are angular velocity and angular acceleration, not inertia. Force is a linear quantity, not the rotational one described by inertia. The distance from the axis is part of how inertia is calculated (through r^2 dm), but inertia itself isn’t just a simple distance—it’s the mass distribution weighted by the square of the radius to the axis.

In formula form, for discrete masses I = Σ m_i r_i^2, and for continuous bodies I = ∫ r^2 dm. This gives the intuition that mass farther from the axis contributes more to inertia, increasing the torque needed for the same angular acceleration.