# Angular acceleration

## Definition[edit | edit source]

Angular acceleration is a vector whose magnitude is defined as the change in angular velocity in unit time.

It is in in SI unit.

## Formula[edit | edit source]

Analogous to translational acceleration, , angular acceleration has the defining formula:

in which represents an *instantaneous* change in angular velocity,which takes place in , a short flitting time.

Equivalently, think about the limiting case:

## Relationship with Constant Torque[edit | edit source]

The angular acceleration of an fixed-axis-object is proportional to the net torque applied.

in which is the Moment of Inertia of the object.

## Angular Kinematics[edit | edit source]

When an rotation has constant angular acceleration , the angle displacement covered in a given time is given by an equation that is strikingly similar to the equation for displacement under constant acceleration.

in which is the angular velocity *at the beginning* of the time period

in which case the angular velocity at the beginning is "zero"

in which is the angular velocity *at the end* of the time period