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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

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.

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.