Angular acceleration.html

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 ( ${\alpha}\,$ ).

1 Mathematical definition
2 Equations of motion
- 2.1 Constant acceleration
- 2.2 Non-constant acceleration
3 See also
4 References
5 External links

Mathematical definition

The angular acceleration can be defined as either:

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

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

where $ω$ 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, Newton's second law can be adapted to describe the relation between torque and angular acceleration:

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

where $τ$ 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, $τ$ , 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.

References

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Angular acceleration.html

Contents

Mathematical definition

Equations of motion

Constant acceleration

Non-constant acceleration

See also

References

External links