Analogue of mass in rotational motion is

The analogue of mass in rotational motion is called moment of inertia. Like mass, moment of inertia determines the resistance of an object to changes in its motion: now to rotational motion instead of linear motion. The property depends not only on the mass of the object but also on how that mass is distributed relative to the axis of rotation.

For example, take the ring and sphere both of identical mass and radius, but let one be an ordinary ring that can be placed outside the edge where the most amount of the mass is localized in comparison with a solid sphere whose mass remains concentrated closer to the axis, resulting in higher moment of inertia of the former over the latter, meaning one will require higher torque to cause angular acceleration if its angular velocity was the same for both.

The moment of inertia is very important in rotational dynamics. It is the rotational counterpart of mass in linear motion. Other quantities such as angular momentum and radius of gyration are related to rotational motion but do not directly represent mass. Angular momentum is like linear momentum in rotation, and the radius of gyration provides a measure of mass distribution. Thus, the moment of inertia is the true rotational equivalent of mass.

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