Moment of inertia

Definition

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on both the mass of the object and how that mass is distributed relative to the axis of rotation.

5 Must Know Facts For Your Next Test

1. Moment of inertia is often denoted by the symbol $I$.
2. The moment of inertia for a point mass is calculated as $I = mr^2$, where $m$ is the mass and $r$ is the distance from the axis of rotation.
3. For extended objects, moment of inertia must be calculated by integrating over the entire volume: $I = \int r^2 dm$.
4. Different shapes have different moments of inertia; for example, a solid sphere has a different moment of inertia than a hollow sphere with the same mass and radius.
5. The parallel axis theorem allows us to find the moment of inertia about any axis parallel to an axis through the center of mass.

Review Questions

• What factors determine an object's moment of inertia?
• How does changing the distribution of mass affect an object's moment of inertia?
• State and explain how you would use the parallel axis theorem to calculate the moment of inertia.

Related terms

Torque:

A measure of how much a force acting on an object causes that object to rotate. Calculated as $\tau = rF\sin(\theta)$.

Angular Momentum:

The quantity of rotation an object has, given by $L = I\omega$, where $\omega$ is angular velocity.

Rotational Kinetic Energy:

$K_{rot} = \frac{1}{2}I\omega^2$, representing the energy due to rotational motion.