$A$ 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 $3 \ s$?

Four masses of $2 \ kg$ each are attached to an axle by spokes of length $1/4 \ m$ as shown in the figure. $A$ force $F = 24 \ N$ is applied at the end of a spoke of length $1/2 \ m$ at an angle of $30^{\circ}$ to produce an angular acceleration $\alpha$. The value of $\alpha$ is ........ $rad/s^2$.

If a force acts on a body at a point away from the center of mass,then:

The moment of inertia of a wheel about its vertical axis is $2 \ kg \ m^2$. It is rotating about this axis at a speed of $60 \ rpm$. What torque must be applied to bring the wheel to rest in $1 \ minute$?

$A$ triangular plate of uniform thickness and density rotates about an axis perpendicular to the plane of the paper. In case $(a)$,the axis passes through point $A$,and in case $(b)$,it passes through point $B$. If an equal force $F$ is applied as shown in the figure,in which case will the angular acceleration be greater?

What does the time rate of change of angular momentum represent?