Inertia Defined by Mass, Radius, and Rotation Axis Moment of inertia measures the resistance of an object to changes in its rotational velocity and is governed by its mass, radius, and how that mass is distributed relative to the rotation axis. A greater mass or a larger radius extends the mass farther from the axis, making angular acceleration more difficult. Examples with wheels and rods show that concentrating mass near the pivot eases rotation.
Shape and Mass Distribution Determine Rolling Speed When a solid sphere, a solid cylinder, and a hollow cylinder of equal mass roll down a ramp, their differing moments of inertia dictate their acceleration. The solid sphere, with a moment of inertia of 2/5 MR², has a lower inertia compared to the solid cylinder’s 1/2 MR² and the hollow cylinder’s MR², allowing it to accelerate faster. This outcome highlights that a lower moment of inertia, driven by mass distribution, provides a competitive edge in rotational motion.