$A$ 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 .... $m/sec^2$.

$A$ 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?

If the angular velocity of a merry-go-round is $60^o/s$ and you are $3.5\,m$ from the centre of rotation,your linear velocity will be

$A$ wheel of radius $30 \ cm$ rotates about its axis and undergoes an angular displacement of $30^\circ$. The linear distance covered by the wheel is .......

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

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 $B$?