$A$ wheel starting from rest gains an angular velocity of $10 \ rad/s$ after being uniformly accelerated for $5 \ s$. The total angle through which it has turned is

The plank in the figure moves a distance $100 \ mm$ to the right while the centre of mass of the sphere of radius $150 \ mm$ moves a distance $75 \ mm$ to the left. The angular displacement of the sphere (in radian) is (there is no slipping anywhere):-

Consider two masses with $m_1 > m_2$ connected by a light inextensible string that passes over a pulley of radius $R$ and moment of inertia $I$ about its axis of rotation. The string does not slip on the pulley and the pulley turns without friction. The two masses are released from rest separated by a vertical distance $2h$. When the two masses pass each other,the speed of the masses is proportional to

$A$ uniform rod of length $l$ is being rotated in a horizontal plane with a constant angular speed $\omega$ about an axis passing through one of its ends. If the tension generated in the rod due to rotation is $T(x)$ at a distance $x$ from the axis,then which of the following graphs depicts it most closely?

In pure translational motion,the velocity of every particle of a body at any instant is what? Equal or unequal?

$A$ ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along $\qquad$