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:

$A$ wheel of radius $4 \, m$ completes one revolution in $2 \, s$. Find the centripetal acceleration of the wheel.

$A$ particle is moving on a circular path with a constant speed $v$. Its change of velocity as it moves from $A$ to $B$ in the figure is

$A$ stone tied to the end of a string of $1\, m$ length is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolutions in $44\, s$,what is the magnitude and direction of the acceleration of the stone?

Two objects of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their respective angular speeds $\omega_1$ and $\omega_2$ are such that they both complete one revolution in the same time $t$. The ratio of the linear speed of $m_2$ to that of $m_1$ is:

$A$ particle moves in a circle of radius $5 \; cm$ with constant speed and time period $0.2 \pi \; sec$. The acceleration of the particle is .... $m/sec^2$.