Uniform Circular Motion

What is the linear velocity if the angular velocity vector is $\overrightarrow{\omega }=3\hat{\mathrm{i}}-4\hat{\mathrm{j}}+\hat{\mathrm{k}}$  and position vector is $\overrightarrow{r}=5\hat{\mathrm{i}}-6\hat{\mathrm{j}}+6\hat{\mathrm{k}}$ ?

The moon revolved about the earth making a complete revolution in $2.36$ Mega second. Assume that the orbit is circular and has a radius of $385$ Mega meter.What is the magnitude of the acceleration of the moon towards the earth?

The velocity of a body moving in a circle in the radical direction is

The earth moves around the Sun in a near circular orbit of radius $1.8\times {10}^{11} \mathrm{m}.$ Its centripetal acceleration is:

The relation between linear and angular velocity is given as

A particle undergoes uniform circular motion. The velocity and angular velocity of the particle at an instant of time is $v=\left(4\hat{\mathrm{i}}+3\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$ and $\omega =\left(x\hat{\mathrm{i}}+8\hat{\mathrm{j}}\right) \mathrm{rad} {\mathrm{s}}^{-1}$. The value of $x$ in $\mathrm{rad} {\mathrm{s}}^{-1}$ is,

If acceleration and velocity of a particle at an instant are $\left(5\overrightarrow{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-2}$ and $(3\overrightarrow{\mathrm{i}}+4\overrightarrow{\mathrm{j}}) \mathrm{m} {\mathrm{s}}^{-1}$ respectively, then the radial acceleration and radius of curvature at that point of the path where particle is present, will be:

Two particles are revolving on circular paths of radii $r_1$ and $r_2$ respectively with same speed. Ratio of their centripetal accelerations is

Mg of ice at $0°$C is to be converted to water at $0°$C. If L is the latent heat of the fusion of ice, the quantity of heat required for the above operation would be

Two bodies A and B are said to be in thermal equilibrium with each other, if

If x is the distance at which a car can be stopped
when initially it was moving with speed u, then
on making the speed of the car $Nu$, the distance
at which the car can be stopped is

The motion of a simple pendulum is

If the mass of a pendulum is doubled, the time period 

The angular velocity of a particle rotating in a circular orbit $100$ times per minute is

The centripetal acceleration required for a particle to move on a circle of radius $r$ with speed $v$ is

A stone is swinging in a horizontal circle $0.8 \mathrm{m}$ in diameter at $30$ $\mathrm{rev} {\min }^{-1}$. A distant light causes a shadow of the stone to be formed on a near by wall. What is the amplitude of the motion of the shadow? What is the frequency?

For a body moving with constant speed in horizontal circle, which of the following remains constant.

A body of mass $100 \mathrm{gm}$ is rotating in a circular path of radius $r$ with constant speed. The work done in one complete revolution is