ANGULAR ACCELERATION

'Angular acceleration' is the rate of change of angular velocity over time. In SI units, it is measured in radians per second squared (rad/s²), and is usually denoted by the Greek letter alpha ().

Contents

Mathematical definition

Equations of motion

Constant acceleration

Non-constant acceleration

See also

Mathematical definition

The angular acceleration can be defined as either:
: , or

: ,
where $\{omega\}$ is the angular velocity, $mathbf\{a\}\_\{T\}$ is the linear tangential acceleration, and r is the radius of curvature.

Equations of motion

For rotational motion, can be adapted to describe the relation between torque and angular acceleration:
: ,
where $\{\; au\}$ is torque, and $I$ is moment of inertia.

Constant acceleration

For all constant values of the torque, $\{\; au\}$, of an object, the angular acceleration will also be constant. For this special case of constant angular acceleration, the above equation will produce a definitive, singular value for the angular acceleration:
: .

Non-constant acceleration

For any non-constant torque, the angular acceleration of an object will change with time. The equation becomes a differential equation instead of a singular value. This differential equation is known as the equation of motion of the system and can completely describe the motion of the object.

See also

★ Angular momentum

★ Angular speed

★ Angular velocity

★ Rotation

★ Spin

★ Angular acceleration article.