$A$ 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 is moving with constant angular acceleration $4 \text{ rad/s}^2$ in a circular path. At what time will the magnitudes of its tangential acceleration and centripetal acceleration be equal (in $\text{ s}$)?

$A$ flywheel rotates with a uniform angular acceleration. Its angular velocity increases from $20\pi \, rad/s$ to $40\pi \, rad/s$ in $10 \, s$. How many rotations did it make in this period?

$A$ wheel has an angular acceleration of $3.0\, rad/s^2$ and an initial angular speed of $2.00\, rad/s$. In a time of $2\, s$,it has rotated through an angle (in radians) of:

$A$ wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of $15^{\circ}$ in time $t \ s$. The increase in angle through which it rotates in the next $2t \ s$ is (in $^{\circ}$)

The angular speed of the wheel of a vehicle is increased from $360 \; rpm$ to $1200 \; rpm$ in $14 \; s$. Its angular acceleration is,