What Is Moment of Inertia?

Moment of Inertia

The moment of inertia is a scalar physical quantity that measures an object’s resistance to rotational motion around an axis. Just as mass determines how much an object resists changes in linear motion, moment of inertia defines how much an object resists changes in rotational motion. It is usually denoted by the letter I or J, and measured in kilogram·meters squared (kg·m²).

Inertia is the property of objects to maintain their state of motion in the absence of external forces. In linear motion, this is quantified by mass: the greater the mass, the harder it is to accelerate or decelerate the object. For example, it’s easier to push a football than to move a car — the car has more mass and therefore greater inertia.

In rotational motion, inertia manifests differently: an object resists changes in its angular velocity — meaning it resists speeding up or slowing down its rotation. This resistance is measured not by mass alone, but by the moment of inertia. If mass tells us how "stubborn" an object is when changing its linear motion, the moment of inertia tells us how stubborn it is to rotational acceleration or deceleration.

When an object rotates, every point in it moves in a circle around the axis. The contribution of each point mass to the overall resistance to rotation depends not only on its mass but also on its distance from the axis. The farther a point is from the axis, the greater its effect on the moment of inertia. This is because greater force (torque) is needed to change the angular velocity at larger radii.