Define Angular Acceleration

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Angular acceleration is defined as the rate of change of angular velocity with respect to time. Angular acceleration represented as ‘α’ is a vector quantity and therefore has both magnitude and direction. When an object moves in a circular path, unlike linear motion where it travels in a straight line path, in circular motion it constantly changes its direction and path to follow the circular curve and this change in angular velocity produces angular acceleration.

Example 1: The angular velocity of an object travelling in a circular path is changing at a rate 40rad/sec. What is the angular acceleration of the object in the time period of 8 seconds?

The formula: Angular acceleration, α = ?ω/?t

Here, ?ω = change in angular velocity = 40rad/sec

?t= time interval = 8 seconds

This gives: Angular acceleration, α = (40rad/sec)/ (8secs)

Hence the angular acceleration of the given object, α = 5 rad/sec2

Example 2: If the instantaneous angular acceleration of an object travelling with an angular
velocity of 21rad/sec is 3rad/sec2, then what is the time at that particular instant?

The formula: Instantaneous Angular acceleration, α = dω/ dt

Given instantaneous angular acceleration, α = 3rad/sec2

 dω = angular velocity at the particular instant = 21rad/sec

dt= time at that instant

This gives: 3 = (21rad/sec)/ (time) ==> time = 21/3 = 7secs.

Hence the time at the particular instant, t = 7 seconds.

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