The moment of inertia of a body about a given axis is $1.2 \ kg \cdot m^2$. Initially,the body is at rest. To produce a rotational kinetic energy of $1500 \ J$,an angular acceleration of $25 \ rad/s^2$ must be applied to the body for a duration of ........ $(s)$.

The engine of a motor vehicle develops a power of $100 \, kW$. If it rotates at a speed of $1800 \, rpm$,the torque exerted by it is ...... $N-m$.

$A$ wheel having a moment of inertia $2 \; kg \cdot m^2$ about its vertical axis rotates at the rate of $60 \; rpm$ about this axis. The torque required to stop the wheel's rotation in one minute is:

$A$ torque of $30 \, N \cdot m$ is applied for $10 \, s$ on a wheel of mass $5 \, kg$ and moment of inertia $2 \, kg \cdot m^2$. The angular displacement of the wheel in $10 \, s$ will be ....... radians.

Two circular discs of radius $10 \ \text{cm}$ each are joined at their centres by a rod of length $30 \ \text{cm}$ and mass $600 \ \text{g}$ as shown in the figure. If the mass of each disc is $600 \ \text{g}$ and the applied torque between the two discs is $43 \times 10^{5} \ \text{dyne cm}$, the angular acceleration of the discs about the given axis $AB$ is . . . . . . $\text{rad/s}^{2}$.

Consider a particle of mass $m$ having linear momentum $\vec{p}$ at position $\vec{r}$ relative to the origin $O$. Let $\vec{L}$ be the angular momentum of the particle with respect to the origin. Which of the following equations correctly relate $\vec{r}, \vec{p}$ and $\vec{L}$?