Angular displacement $(\theta)$ of a flywheel varies with time as $\theta = at + bt^2 + ct^3$. The angular acceleration is given by:

If a wheel starting from rest is rotating with an angular acceleration of $\pi \ rad \ s^{-2}$,then the number of rotations made by the wheel in the first $6 \ s$ is:

$A$ car changes speed from $18\,km/h$ to $36\,km/h$ in $5\,s$. The diameter of its wheel is $0.8\,m$. The angular acceleration of the wheel is ........ $rad/s^2$.

If the length of the second's hand in a stop clock is $3 \, cm$,the angular velocity and linear velocity of the tip are:

$A$ ball is spun with angular acceleration $\alpha = 6t^2 - 2t$,where $t$ is in seconds and $\alpha$ is in $rad/s^2$. At $t = 0$,the ball has an angular velocity of $10 \ rad/s$ and an angular position of $4 \ rad$. The most appropriate expression for the angular position of the ball is:

$A$ particle at rest starts moving with constant angular acceleration '$\alpha$' in a circular path of radius '$r$'. At a certain instant, the magnitude of centripetal acceleration is $(1/3)^{rd}$ the tangential acceleration. The relation between linear speed $(V)$ and angular acceleration $(\alpha)$ is