The rate at which the angular velocity changes with time is known as the angular acceleration in circular motion. It is also known as rotational acceleration. The quantity has both magnitude and direction, so it is a vector quantity.
Angular acceleration is denoted by α.
Let θ be the angular displacement,
ω�
be the angular velocity and α, be the angular acceleration, then;
α=dωdt=d2θdt2�=����=�2���2
(as;
ω=dθdt�=����
)
The above formula can be used to calculate a constant angular acceleration.
If
ΔωΔ�
is the change in angular velocity over a time interval
ΔtΔ�
, then the average angular acceleration is given by:
α=ΔωΔt�=Δ�Δ�
The average value and the instantaneous value coincide for uniform rotation.
The units are rad/s2 or radians per second squared.
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