$A$ wheel rotates with a uniform angular acceleration of $2.0 \ rad/s^2$. If the wheel starts from rest,the number of revolutions completed in the first $10 \ s$ will be approximately:

The relative angular speed of the hour hand and the second hand of a clock is:

If the angular velocity of a disc depends on the angle rotated $\theta$ as $\omega = \theta^2 + 2\theta$,then its angular acceleration $\alpha$ at $\theta = 1 \text{ rad}$ is ......... $\text{rad/sec}^2$.

$A$ particle is rotating in a circular path and at any instant its motion can be described as $\theta = \frac{5t^4}{40} - \frac{t^3}{3}$. The angular acceleration of the particle after $10 \text{ s}$ is . . . . . . $\text{rad/s}^2$.

$A$ particle at rest starts moving with a constant angular acceleration of $4 \ rad/s^2$ in a circular path. The time at which the magnitudes of its centripetal acceleration and tangential acceleration will be equal is (in seconds):

An electric fan has blades of length $30 \, cm$ as measured from the axis of rotation. If the fan is rotating at $1200 \, r.p.m.$,the acceleration of a point on the tip of the blade is about .......... $m/s^2$.