The angular acceleration of a wheel is $3 \ rad/s^2$. If its initial angular velocity is $2 \ rad/s$,what is the angular displacement (in $rad$) covered by it in $2 \ s$?

If the speed of a particle moving in a circle of radius $2 \ m$ is given as $v = 2t + 2$,then its centripetal acceleration after $1 \ s$ will be ......... $m/s^2$.

Certain neutron stars are believed to be rotating at about $1 \, rev/sec$. If such a star has a radius of $20 \, km$,the acceleration of an object on the equator of the star will be:

$A$ ceiling fan starts from rest and makes $10$ revolutions in the first $3$ seconds. If the angular acceleration remains constant,how many revolutions will it make in the next $3$ seconds?

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 of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as $a_c = k^2rt^2$,where $k$ is a constant. What is the power delivered to the particle by the force acting on it?