$A$ wheel of radius $30 \ cm$ is driven by a belt. Its initial angular speed is $2 \ rev/s$. Starting at this speed,it comes to rest after a length of $25 \ m$ of the belt has passed over the wheel. The angular deceleration of the wheel is ....... $rad \ s^{-2}$.

$A$ wheel,initially at rest,is rotated with a uniform angular acceleration. The wheel rotates through an angle ${\theta _1}$ in the first $1 \ s$ and through an additional angle ${\theta _2}$ in the next $1 \ s$. The ratio $\frac{{\theta _2}}{{\theta _1}}$ is

The linear speed of the tip of the seconds hand of a wall clock is $1.05 \, cm \, s^{-1}$. The length of the seconds hand is nearly ........ $cm$.

The angular speed of a flywheel moving with uniform angular acceleration changes from $1200\,rpm$ to $3120\,rpm$ in $16\,s$. The angular acceleration in $rad/s^{2}$ is: (in $\pi$)

$A$ racing car is travelling along a track at a constant speed of $40\ m/s$. $A$ $T.V.$ cameraman is recording the event from a distance of $30\ m$ directly away from the track as shown in the figure. In order to keep the car under view in the position shown,the angular speed with which the camera should be rotated is ........ $rad/s$.

The direction of angular acceleration of a body moving in a circle in the plane of the paper is