$A$ wheel has a diameter of $1 \ m$. If it makes $30$ revolutions per second,then the linear speed of a point on its circumference will be:

Obtain the equation $\omega = \omega_{0} + \alpha t$ from first principles.

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

$A$ fan rotating with an angular speed of $600 \, rev/min$ comes to rest after $60$ revolutions when switched off. The time taken to come to rest is ........ $(sec)$.

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 .......... $m/s^2$.

$A$ wheel is rotating at $900 \, r.p.m.$ about its axis. When the power is cut-off,it comes to rest in $1 \, minute$. The angular retardation in $rad/s^2$ is: