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) $$ \omega=\gamma=0.4 rad/s$$
