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 at rest. Its angular velocity increases uniformly and becomes $60 \ rad/sec$ after $5 \ sec$. The total angular displacement is ........ $rad$.

$A$ ceiling fan starts from rest and makes $10$ revolutions in the first $3$ seconds. If the angular acceleration remains constant,how many revolutions will it make in the next $3$ seconds?

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 at $t = 2 \, s$ is:

Identify the increasing order of the angular velocities of the following:
$1$. Earth rotating about its own axis
$2$. Hour hand of a clock
$3$. Second hand of a clock
$4$. Flywheel of radius $2 \ m$ making $300 \ rpm$

Three particles $A, B$ and $C$ move in a circle of radius $r = \frac{1}{\pi} \, m$ in the anticlockwise direction with speeds $1 \, m/s$,$2.5 \, m/s$ and $2 \, m/s$ respectively. The initial positions of $A, B$ and $C$ are as shown in the figure. The ratio of the distance travelled by $B$ and $C$ by the instant $A, B$ and $C$ meet for the first time is