The relative angular speed of the hour hand and the second hand of a clock is:

$A$ particle moves along a circle of radius $\left( \frac{20}{\pi} \right) \, m$ with constant tangential acceleration. If the velocity of the particle is $80 \, m/s$ at the end of the second revolution after motion has begun,the tangential acceleration is

Three particles $A, B$ and $C$ move in a circle of radius $r = \frac{1}{\pi} \, m$ in the anticlockwise direction with speeds $1 \, m/s$,$2.5 \, m/s$ and $2 \, m/s$ respectively. The initial positions of $A, B$ and $C$ are as shown in the figure. The ratio of the distance travelled by $B$ and $C$ by the instant $A, B$ and $C$ meet for the first time is

$A$ particle performing $U.C.M.$ of radius $\frac{\pi}{2} \ m$ makes $x$ revolutions in time $t$. Its tangential velocity is

The angular acceleration of a body, moving along the circumference of a circle, is :

The angular speed of the wheel of a vehicle is increased from $360 \; rpm$ to $1200 \; rpm$ in $14 \; s$. Its angular acceleration is,