Angular acceleration


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


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