As a wheel turns, the angle through which it has turned varies with time as β(t)=Ct + Bt3 where C=0.400rad/s and B=0.0120rad/s3. Calculate the angular velocity w(t) as a function of time.

ω(t) = 0.4 + 0.036 t²

Explanation:  

The angular displacement of the disk is given as the function of time:

β(t) = Ct + B t³

where,

C = 0.4 rad/s

B = 0.012 rad/s³

Therefore,

β(t) = 0.4 t + 0.012 t³

Now, for angular velocity ω(t), we must take derivative of angular displacement with respect to t:

ω(t) = dβ/dt = (d/dt)(0.4 t + 0.012 t³)

ω(t) = 0.4 + 0.036 t²