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:

If the kinetic energy $(KE)$ of a particle of mass $m$ performing uniform circular motion $(UCM)$ in a circle of radius $r$ is $E$,find the acceleration of the particle.

$A$ particle revolving in a circular path travels the first half of the circumference in $4 \ s$ and the next half in $2 \ s$. What is its average angular velocity?

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 $^{\circ}$)

$A$ particle undergoes uniform circular motion. About which point on the plane of the circle will the angular momentum of the particle remain conserved?

If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass $m$ having position vector $\vec{r} = a(\hat{i} \cos \omega t + \hat{j} \sin \omega t)$,the direction of the force acting on the particle is: