Which of the following quantities remains constant during uniform circular motion?

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

$A$ merry-go-round rotating at a constant angular speed completes $9$ rotations in $18$ seconds. What is its angular speed?

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:

Write the relation between linear speed and angular speed.

$A$ body performing uniform circular motion of radius $R$ has frequency $n$. Its centripetal acceleration is