Angular acceleration is the rate of change of angular velocity. In SI units, it is measured in radians per second squared (rad/s^{2}), and is usually denoted by the Greek letter alpha (

Consider the following situations in which angular velocity is not constant: when a skater pulls in her arms, when a child starts up a merry-go-round from rest, or when a computer's hard disk slows to a halt when switched off. In all these cases, there is an angular acceleration in which

where ^{2}. If

It is useful to know how linear and angular acceleration are related. In circular motion, there is acceleration that is *tangent* to the circle at the point of interest (as seen in the diagram below). This acceleration is called *tangential acceleration,* a_{t}.

## Tangential acceleration

In circular motion, acceleration can occur as the magnitude of the velocity changes: a is tangent to the motion. This acceleration is called tangential acceleration.

Tangential acceleration refers to changes in the magnitude of velocity but not its direction. In circular motion, centripetal acceleration, a_{c}, refers to changes in the direction of the velocity but not its magnitude. An object undergoing circular motion experiences centripetal acceleration (as seen in the diagram below.) Thus, a_{t} and a_{c} are perpendicular and independent of one another. Tangential acceleration a_{t} is directly related to the angular acceleration and is linked to an increase or decrease in the velocity (but not its direction).

## Centripetal Acceleration

Centripetal acceleration occurs as the direction of velocity changes; it is perpendicular to the circular motion. Centripetal and tangential acceleration are thus perpendicular to each other.