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 \(t=0\) $$ \omega=\gamma=0.4 rad/s$$

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