What is the direction of velocity at any point on the circle for a particle undergoing uniform circular motion?

$A$ particle moves such that its position vector $\overrightarrow{r}(t) = \cos \omega t \hat{i} + \sin \omega t \hat{j}$,where $\omega$ is a constant and $t$ is time. Which of the following statements is true for the velocity $\overrightarrow{v}(t)$ and acceleration $\overrightarrow{a}(t)$ of the particle?

The shaft of a motor rotates at a constant angular velocity of $3000 \ rpm$. The number of radians it has turned through in $1 \ s$ is (in $\pi$)

$A$ particle is moving in $U.C.M.$ with speed $V$ and radius $R$. The angular acceleration of the particle is

An object moves at a constant speed along a circular path in the horizontal $XY$ plane with the center at the origin. When the object is at $x = -2 \, m$,its velocity is $-(4 \, m/s) \hat{j}$. What is the object's acceleration when it is at $y = 2 \, m$?

Two cars $A$ and $B$ are moving along concentric circular paths of radii $R_A$ and $R_B$. If both cars complete their respective circular paths in the same time,what is the ratio of the angular speed of $A$ to that of $B$?