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A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to $$\theta(t)=\gamma t+\beta t^3$$ where $$\gamma=0.4rad/s$$ and $$\beta=0.0120 rad/s^3$$. What is the initial value of the angular velocity?
Discussion:

The angle through which the merry-go-round has turned varies with time according to $$\theta(t)=\gamma t+\beta t^3$$ where $$\gamma=0.4rad/s$$ and $$\beta=0.0120 rad/s^3$$.

$$\omega=\frac{d\theta}{dt}$$

At $$t=0$$ $$\omega=\gamma=0.4 rad/s$$