Afan blade rotates with angular velocity given by ωz(t)= γ − β t2, where γ = 5.20 rad/s and β = 0.810 rad/s3 . calculate the angular acceleration as a function of time t in terms of β and γ.

Answer : The angular acceleration is

Solution : Given,

The given angular velocity equation is,

At t = 0,    

At t = t,      

Angular acceleration : It is defined as the rate of change of angular velocity with respect to time.

Formula used for angular acceleration :

where,

= angular acceleration

= angular velocity at time 't'

= angular velocity at time '0'

t = time

Now put all the given values in this formula, we get the angular acceleration.

Therefore, the angular acceleration is

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