Describe the rotation of a system with respect to time using angular displacement, angular velocity, and angular acceleration.

Angular displacement is the measurement of the angle, in radians, through which a point on a rigid system rotates about a specified axis.

A rigid system is one that holds its shape but in which different points on the system move in different directions during rotation. A rigid system cannot be modeled as an object.

One direction of angular displacement about an axis of rotation – clockwise or counterclockwise – is typically indicated as mathematically positive, with the other direction becoming mathematically negative.

If the rotation of a system about an axis may be well described using the motion of the system’s center of mass, the system may be treated as a single object. For example, the rotation of Earth about its axis may be considered negligible when considering the revolution of Earth about the center of mass of the Earth–Sun system.

Angular velocity is the rate at which angular position changes with respect to time.

Angular acceleration is the rate at which angular velocity changes with respect to time.

Angular displacement, angular velocity, and angular acceleration around one axis are analogous to linear displacement, velocity, and acceleration in one dimension and demonstrate the same mathematical relationships.

For constant angular acceleration, the mathematical relationships between angular displacement, angular velocity, and angular acceleration can be described with the following equations:

Graphs of angular displacement, angular velocity, and angular acceleration as functions of time can be used to find the relationships between those quantities.