# Angular acceleration

Template:Infobox unit Template:Classical mechanics Angular acceleration is the rate of change of angular velocity. In SI units, it is measured in radians per second squared (rad/s2), and is usually denoted by the Greek letter alpha (α).

## Mathematical definition

The angular acceleration can be defined as either:

${\alpha }={\frac {d\omega }{dt}}={\frac {d^{2}{\theta }}{dt^{2}}}$ , or
${\alpha }={\frac {a_{T}}{r}}$ ,

## Equations of motion

For two-dimensional rotational motion (constant ${\hat {L}}$ ), Newton's second law can be adapted to describe the relation between torque and angular acceleration:

${\tau }=I\ {\alpha }$ ,

### Constant acceleration

For all constant values of the torque, ${\tau }$ , 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, constant value for the angular acceleration:

${\alpha }={\frac {\tau }{I}}.$ ### 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 constant value. This differential equation is known as the equation of motion of the system and can completely describe the motion of the object. It is also the best way to calculate the angular velocity.