Find the angle between the velocity vector and the acceleration vector for a particle in uniform circular motion. (in $^{\circ}$)

$A$ motor shaft rotates at a constant angular velocity of $3000$ revolutions per minute. Through what angle (in radians) will it rotate in $1$ second?

$A$ particle moves so that its position vector is given by $\vec{r} = \cos(\omega t) \hat{i} + \sin(\omega t) \hat{j}$,where $\omega$ is a constant. Which of the following is true?

$A$ fan is making $600$ revolutions per minute. If after some time it makes $1200$ revolutions per minute,then the increase in its angular velocity is

$A$ particle revolving in a circular path travels the first half of the circumference in $4 \ s$ and the next half in $2 \ s$. What is its average angular velocity?

$A$ particle moves in a circle of radius $25\, cm$ at two revolutions per second. The acceleration of the particle in $m/s^2$ is