When an object is travelling on a circular path, it constantly changes its direction due to the curvy path. This constant change in the direction of the velocity causes the acceleration and this acceleration is known as the angular acceleration. Therefore angular acceleration is described as the change in the angular velocity with respect to change in time. Instantaneous angular acceleration also implies the same definition, but here the angular velocity is considered at a given particular instant of time. Angular acceleration is a vector quantity since it has both magnitude and direction.
Example 1: The angular velocity of an object travelling in a circular path is changing at a rate 15rad/sec. Calculate the angular acceleration of the object in a time interval of 5secs.
The formula is given by: Angular acceleration, α = ?ω/?t
Here, ?ω = change in the angular velocity = 15rad/sec
?t= change in time or time interval = 5secs
This gives: Angular acceleration, α = (15rad/sec)/ (5secs)
Hence the angular acceleration of the given object, α = 3 rad/sec2
Example 2: What is the instantaneous angular acceleration of an object travelling with an angular
velocity of 38rad/sec at the instant when the time is 8secs?
The formula is given by: Instantaneous Angular acceleration, α = dω/ dt
Given: dω = angular velocity at the particular instant = 38rad/sec
dt= time at a particular instant = 8secs
This gives: α = (38rad/sec)/ (8secs)
==> Instantaneous angular acceleration, α = 38/8 = 4.75 rad/sec2
Hence the instantaneous angular acceleration of the object is 4.75 rad/sec2