The angular velocity of a particle is given by $\omega = 1.5t - 3t^2 + 2$. How much time in $sec$ does it take for the angular acceleration to become zero?

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:

$A$ particle of mass $m$ moves along a circle of radius $r$ with constant tangential acceleration. If the kinetic energy $E$ of the particle becomes three times by the end of the third revolution after the beginning of the motion,then the magnitude of the tangential acceleration is:

The wheel of a car is rotating at the rate of $1200$ revolutions per minute. On pressing the accelerator for $10 \ s$,it starts rotating at $4500$ revolutions per minute. The angular acceleration of the wheel is:

$A$ particle moves from point $P_1$ to $P_2$ along a circular path with constant speed $v$. If the angle subtended by the arc $P_1P_2$ at the center is $90^{\circ}$,what is the change in velocity?

$A$ particle moves along a circle of radius $\left( \frac{20}{\pi} \right) \, m$ with constant tangential acceleration. If the velocity of the particle is $80 \, m/s$ at the end of the second revolution after motion has begun,the tangential acceleration is