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

$A$ particle moves with a constant speed $v$ along a circle of radius $R$. What is the change in velocity of the particle as it moves from point $P_1$ to $P_2$?

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:

For a particle in uniform circular motion,the acceleration $\vec{a}$ at any point $P (R, \theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x$-axis and $v$ is uniform speed):

$A$ ball is moving uniformly in a circular path of radius $1 \, m$ with a time period of $1.5 \, s$. If the ball is suddenly stopped at $t = 8.3 \, s$,the magnitude of the displacement of the ball with respect to its position at $t = 0 \, s$ is closest to .......... $m$.

$A$ particle performing uniform circular motion of radius $\frac{\pi}{2} \,m$ makes $x$ revolutions in time $t$. Its tangential velocity is