$A$ wheel having a moment of inertia of $200 \ kg \cdot m^2$ about its axis passing through its center is rotated by a constant torque of $1000 \ N \cdot m$. What will be its angular velocity in $rad/s$ after $3 \ s$?

$A$ constant torque of $31.4 \, Nm$ is exerted on a pivoted wheel. If the angular acceleration of the wheel is $4\pi \, rad/s^2$,then the moment of inertia will be ....... $kg \cdot m^2$.

In the following figure,$r_1 = 5\,cm$ and $r_2 = 30\,cm$. If the moment of inertia of the wheel is $1500\,kg\cdot m^2$,then its angular acceleration will be (approximately):

$A$ torque of $10^5 \ N \cdot m$ is applied to a disc of mass $10 \ kg$ and radius of gyration $50 \ m$. What is the value of the angular acceleration in $rad/s^2$?

$A$ rigid massless rod of length $3l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis (see figure). When released from the initial horizontal position,its instantaneous angular acceleration will be

The moment of inertia of a body about a given axis is $2.4 \, kg \cdot m^2$. For what duration of time must an angular acceleration of $5 \, rad/s^2$ be applied about this axis to generate a rotational kinetic energy of $750 \, J$? (in seconds)