Consider a rigid body made up of many infinitesimal particles in rotational motion. Its kinetic energy can be related to its rotational speed. Using the moment of inertia notation, the rotational kinetic energy of the body is observed to be proportional to the moment of inertia and the square of the angular velocity. It is similar to how the kinetic energy of a rigid body in translational motion is proportional to its mass and the square of the linear velocity. A body with a greater moment of inertia will gain more kinetic energy when it is sped up by the same angular speed. Hence, more work would need to be done to change its angular speed. Thus, the moment of inertia gives a quantitative measure of rotational inertia.