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 ($\{alpha\},$).

Mathematical definition

The angular acceleration can be defined as either:

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

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

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:

:$\{\; au\}\; =\; I\; \{alpha\}$ ,where $\{\; au\}$ 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, $\{\; au\}$, 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, constant value for the angular acceleration:

:$\{alpha\}\; =\; frac\{\; au\}\{I\}$ .

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.

See also

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

References

External links