Angular acceleration

Angular acceleration
Common symbols	α
SI unit	rad/s2
In SI base units	s−2
Behaviour under coord transformation	pseudovector
Dimension	${\displaystyle {\mathsf {T}}^{-2}}$

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${\displaystyle {\textbf {F}}={\frac {d}{dt}}(m{\textbf {v}})}$ Second law of motion
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In physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity. Following the two types of angular velocity, spin angular velocity and orbital angular velocity, the respective types of angular acceleration are: spin angular acceleration, involving a rigid body about an axis of rotation intersecting the body's centroid; and orbital angular acceleration, involving a point particle and an external axis.

Angular acceleration has physical dimensions of angle per time squared, measured in SI units of radians per second squared (rad ⋅ s^-2). In two dimensions, angular acceleration is a pseudoscalar whose sign is taken to be positive if the angular speed increases counterclockwise or decreases clockwise, and is taken to be negative if the angular speed increases clockwise or decreases counterclockwise. In three dimensions, angular acceleration is a pseudovector.^[1]

For rigid bodies, angular acceleration must be caused by a net external torque. However, this is not so for non-rigid bodies: For example, a figure skater can speed up their rotation (thereby obtaining an angular acceleration) simply by contracting their arms and legs inwards, which involves no external torque.