Moment of inertia

Definition

Moment of inertia is a measure of an object's resistance to changes in its rotational motion about a fixed axis. It depends on the mass distribution relative to the axis of rotation.

5 Must Know Facts For Your Next Test

1. 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.
2. For extended bodies, the moment of inertia is found by integrating $r^2 \, dm$ over the entire mass distribution.
3. The Parallel Axis Theorem states that $I = I_{cm} + Md^2$, where $I_{cm}$ is the moment of inertia about the center of mass, $M$ is the total mass, and $d$ is the distance between axes.
4. A higher moment of inertia implies greater resistance to rotational acceleration under an applied torque.
5. Common moments of inertia include that for a solid sphere ($I = \frac{2}{5}MR^2$) and a thin rod about its end ($I = \frac{1}{3}ML^2$).

Review Questions

• How do you calculate the moment of inertia for a point mass?
• What does the Parallel Axis Theorem state?
• Why does an object with a higher moment of inertia resist changes in rotational motion more than one with a lower moment?

Related terms

Rotational Kinetic Energy:

Energy possessed by a rotating object, given by $K = \frac{1}{2} I \omega^2$, where $\omega$ is angular velocity.

Torque:

A force that causes an object to rotate around an axis, given by $\tau = rF\sin(\theta)$.

Angular Momentum:

The rotational analogue to linear momentum, defined as $L = I \omega$, where $L$ is angular momentum and $\omega$ is angular velocity.