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Angular Acceleration Formulas Online - Tutorpace

# 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,