The relative angular speed of the hour hand and the second hand of a clock is (in $rad/s$):

The angular speed of a wheel increases from $600 \, rpm$ to $1200 \, rpm$ in $10 \, s$. What is the angular acceleration?

The direction of angular acceleration of a body moving in a circle in the plane of the paper is

If the equation for the angular displacement of a particle moving on a circular path is given by $\theta = 2t^3 + 0.5$,where $\theta$ is in radians and $t$ is in seconds,then the angular velocity of the particle after $2 \ s$ from its start is ......... $rad/s$.

The angular speed of a motor wheel is increased from $1200 \; rpm$ to $3120 \; rpm$ in $16 \; s$.
$(i)$ What is its angular acceleration,assuming the acceleration to be uniform?
$(ii)$ How many revolutions does the engine make during this time?

The angular displacement of a body performing circular motion is given by $\theta = 5 \sin \frac{\pi t}{6}$. The angular velocity of the body at $t = 3 \ s$ will be $\left[\sin \frac{\pi}{2} = 1, \cos \frac{\pi}{2} = 0\right]$.