Motion of a particle in $x-y$ plane is described by a set of following equations $x=4 \sin \left(\frac{\pi}{2}-\omega t\right) \text{ m}$ and $y=4 \sin (\omega t) \text{ m}$. The path of the particle will be:

In Uniform Circular Motion ($U$.$C$.$M$.),when the time interval $\delta t \rightarrow 0$,the angle between the change in velocity $(\delta v)$ and the linear velocity $(v)$ will be (in $^{\circ}$)

State the $SI$ units of angular velocity and angular acceleration.

The angle between velocity and acceleration of a particle describing uniform circular motion is (in $^{\circ}$)

$A$ point $P$ is moving in uniform circular motion with radius $3 \ m$. Let at some instant the acceleration of the point be $a = (6 \hat{i} - 4 \hat{j}) \ m/s^2$, the position vector be $r$, and the velocity vector be $v$. Choose the correct statement.

The figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting $A$ and $B$ do not slip on the wheels. If $x$ and $y$ are the distances travelled by $A$ and $B$ in the same time interval,then