Rotational inertia

Definition

Rotational inertia, also known as the moment of inertia, is a measure of an object's resistance to changes in its rotational motion about an axis. It depends on the object's mass distribution relative to the axis of rotation.

5 Must Know Facts For Your Next Test

1. 1. Rotational inertia is denoted by the symbol $I$ and has units of $kg \cdot m^2$.
2. 2. The moment of inertia for a point mass is given by $I = mr^2$, where $m$ is the mass and $r$ is the distance from the axis of rotation.
3. 3. An object's rotational inertia increases with more mass further from the axis of rotation.
4. 4. For complex shapes, the total moment of inertia can be found by summing or integrating individual moments of inertia.
5. 5. Rotational inertia plays a crucial role in Newton's second law for rotation: $\tau = I\alpha$, where $\tau$ is torque and $\alpha$ is angular acceleration.

Review Questions

• What factors affect an object's rotational inertia?
• What is the relationship between torque, rotational inertia, and angular acceleration?
• How would you calculate the moment of inertia for a uniform disc rotating about its center?

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 Acceleration: The rate at which an object's angular velocity changes with time, typically denoted by $\alpha$.

Radius of Gyration: A measure that describes how far from the axis all of an object's mass could be concentrated without changing its moment of inertia, defined as $k = \sqrt{I/m}$.