$A$ particle is moving on a circular path of radius $r$ with uniform speed $v$. The change in velocity when the particle moves from $P$ to $Q$ is $(\angle POQ = 40^\circ)$.

The magnitude of displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as:

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.

An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rotating with a uniform angular speed $\omega$ about its central axis. The ratio of the centripetal forces experienced by two particles of equal mass $m$ situated on the inner and outer parts of the ring,$\frac{F_{1}}{F_{2}}$ is

Give an example of a motion where the object has acceleration but is still considered to have uniform motion.

$A$ particle is performing uniform circular motion. The velocity of the particle at an instant of time is $(6 \hat{i} - 2 \hat{j}) \ m/s$ and the angular velocity is $\vec{\omega} = (a \hat{i} + b \hat{j}) \ rad/s$. Then the value of $\frac{b}{a}$ is: