$A$ 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 ....... $rad \ s^{-2}$.

$A$ particle revolves with constant angular acceleration $\pi \, rad/s^2$. If the particle starts from rest,how many revolutions will it make in the first $10 \, s$?

If the frequency of an object in uniform circular motion is doubled,its acceleration becomes

The angular speed of a truck wheel is increased from $900 \, rpm$ to $2460 \, rpm$ in $26 \, s$. The number of revolutions made by the truck engine during this time is (assuming the acceleration to be uniform).

$A$ particle moves along a circular path of radius $r = \frac{20}{\pi} \ m$ with a constant tangential acceleration. If the velocity of the particle at the end of the second revolution is $80 \ m/s$,what is the tangential acceleration?

$A$ particle at rest starts moving with constant angular acceleration '$\alpha$' in a circular path of radius '$r$'. At a certain instant, the magnitude of centripetal acceleration is $(1/3)^{rd}$ the tangential acceleration. The relation between linear speed $(V)$ and angular acceleration $(\alpha)$ is