# Angular acceleration

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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 ($\left\{alpha\right\},$).

Mathematical definition

The angular acceleration can be defined as either:

:$\left\{alpha\right\} = frac\left\{d\left\{omega\left\{dt\right\} = frac\left\{d^2\left\{ heta\left\{dt^2\right\}$ , or

:$\left\{alpha\right\} = frac\left\{mathbf\left\{a\right\}_\left\{T\left\{r\right\}$ ,

where $\left\{omega\right\}$ is the angular velocity, $mathbf\left\{a\right\}_\left\{T\right\}$ 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:

:$\left\{ au\right\} = I \left\{alpha\right\}$ ,where $\left\{ au\right\}$ is the total torque exerted on the body, and $I$ is the mass moment of inertia of the body.

Constant acceleration

For all constant values of the torque, $\left\{ au\right\}$, 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:

:$\left\{alpha\right\} = frac\left\{ au\right\}\left\{I\right\}$ .

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.

* Angular momentum
* Angular speed
* Angular velocity
* Rotation
* Spin

References

Wikimedia Foundation. 2010.

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