$A$ particle $P$ is moving in a circle of radius $a$ with a uniform speed $u$. $C$ is the centre of the circle and $AB$ is the diameter. The angular velocity of $P$ about $A$ and $C$ are in the ratio:

$A$ particle moves such that its position vector $\overrightarrow{r}(t) = \cos \omega t \hat{i} + \sin \omega t \hat{j}$,where $\omega$ is a constant and $t$ is time. Which of the following statements is true for the velocity $\overrightarrow{v}(t)$ and acceleration $\overrightarrow{a}(t)$ of the particle?

The angular speed of a flywheel making $120 \, \text{revolutions/minute}$ is:

$A$ particle moving with uniform speed in a circular path maintains:

Find the angular speed of the hour hand of a clock.

$A$ particle is moving along a circle such that it completes one revolution in $40 \, s$. In $2 \, \text{minutes} \, 20 \, s$, the ratio $\frac{|\text{displacement}|}{\text{distance}}$ is: