Angular Acceleration Formula

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Angular acceleration of an object is the rate of change of angular velocity with respect to the time. It is similar to the linear acceleration but in a circular path.

It is denoted by alpha “α” and its S.I unit is radian/sec^2 or rad/s^2.
                   α = dω/dt
                   α = (ω2 – ω1)/(t2 – t1)

ω = v/r
          and, ω = θ/t
Where,       ω = angular velocity
                   t = time taken
                   v = linear velocity
                   r = radius of circular path
                   θ = rotated angle
          ω1 and ω2 are the two different angular velocity at time t1 and t2 respectively.

Therefore,
                   α = d^2θ/dt^2

Example1: An object is rotating according to the function θ(t) = t3 + t, find the angular acceleration when t = 4 seconds?
Solution:   Given that,
                   Function of angular displacement, θ(t) = t3 + t
                   Time taken, t = 4 sec

Now, we have the equation for angular acceleration.
                   α = d^2θ/dt^2
                   = 6t = 6(4) = 24 rad/sec^2.


Example2: If an object changes it angular velocity from 20 rad/s to 50 rad/s in 6 seconds. Calculate angular acceleration?

Solution: Given that,
                  Angular velocity = 20 rad/s and 50 rad/s
                  Time = 6 sec
Now, we can use the formula for angular acceleration,
                   α = (ω2 – ω1)/(t2 – t1)
                   = (50 – 20)/6 = 30/6 = 5 rad/s^2.


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