A car is going round a circle of radius $R_1$ with constant speed. Another car is going round a circle of radius $R_2$ with constant speed. If both of them take same time to complete the circles, the ratio of their angular speeds and linear speeds will be .........

A particle moves with constant angular velocity in circular path of certain radius and is acted upon by a certain centripetal force $F$. if the centripetal force $F$ is kept constant but the angular velocity is doubled, the new radius of the path (original radius $R$ ) will be

Two particles, one at the centre of a circle of radius $R$, and another at a point $Q$ on the circle, start moving towards a point $P$ on the circle at the same time (see figure below). Both are at rest initially and move with uniform velocities $\vec{V}_1$ and $\overrightarrow{V_2}$ respectively. They also reach the point $P$ at the same time, If the angle between the velocities is $\theta$ and the angle subtended by $P$ and $Q$ at the centre is $\phi$ (as shown in the figure), then

The radius of circle the period of revolution initial position and sense of revolution are indicated in the figure.

$y-$projection of the radius vector of rotating particle $\mathrm{P}$ is

Can you associate vectors with $(a)$ the length of a wire bent into a loop, $(b)$ a plane area, $(c)$ a sphere ? Explain.

A cyclist starts from centre 0 of a circular park of radius $1\, km$ and, moves along the path $OPRQO$ as shown in figure.

If he maintains constant speed of $10\, ms^{-1}$, what is his acceleration at point $R$ in magnitude and direction ?