Write the formula for power and angular momentum in rotational motion.

A disc is rotating with angular velocity $\vec{\omega}$. A force $\vec{F}$ acts at a point whose position vector with respect to the axis of rotation is $\vec{r}$. The power associated with torque due to the force is given by ……….

$A$ rod hinged at one end is released from the horizontal position as shown in the figure. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then the maximum angle $‘\theta ’$ made by the hinged upper half with the vertical is ……… $^o$.

To maintain a rotor at a uniform angular speed of $200 \;rad s^{-1}$, an engine needs to transmit a torque of $180 \;N m .$ What is the power required by the engine?

(Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is $100 \%$ efficient.

A disc is rolling without slipping on a straight surface. The ratio of its translational kinetic energy to its total kinetic energy is