Uniform Circular Motion

A hemispherical bowl of radius $R=0.1 \mathrm{m}$ is rotating about its own axis (which is vertical), with an angular velocity $\omega$. A particle of mass ${10}^{-2} \mathrm{kg}$ on the frictionless inner surface of the bowl is also rotating with the same $\omega$. The particle is at a height $h$ from the bottom of the bowl.
Obtain the relation between $h$ and $\omega$. What is the minimum value of $\omega$ needed, in order to have a non-zero value of $h$ ?

An electric line of force in the $x-y$ plane is given by the equation $x^2+y^2=1$. A particle with unit positive charge, initially at rest at the point $x=1,y=0$ in the $x-y$ plane, will move along the circular line of force.

What is the relation between time period and frequency in case of uniform circular motion?

Define period of revolution of uniform circular motion. Derive an expression for the period of revolution of a particle performing uniform circular motion.

For an object under uniform circular motion, which of the following remains constant

Define frequency of uniform circular motion

The angular displacement of a particle, rotating with constant angular acceleration is $\theta =14 t+4 t^2; \theta$ is measured in radian and $t$ in second. The angular acceleration of the particle is,

A rod of length $L$ is pivoted at one end and is rotated with a uniform angular velocity, in a horizontal plane. Let $T_1$ and $T_2$ be the tensions at points $\frac{L}{4}$ and $\frac{3L}{4}$, away from the pivoted ends.

A particle when moves in a circle with a uniform speed:

Two spheres of equal masses are attached to a string of length $2 \mathrm{m}$ as shown in figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant rate. What is the value of the ratio of the tension in the string between $P$ and $Q$ with the tension in the string between $P$ and $O$?

A stone tied to one end of rope and rotated in a circular motion. If the string suddenly breaks, then the stone travels

The angle turned by a body undergoing circular motion depends on time as $\theta ={\theta }_0+{\theta }_{1}t+{\theta }_2{t}^2$, Then the angular acceleration of the body is :

In a carnival ride the passengers travel in a circle of radius 5.0 m, making one complete circle in 4 s. What is the acceleration?

A racer is moving with a constant tangential speed of $5.65 {\mathrm{ms}}^{-1}$, takes one lap around a circular track of radius $2 \mathrm{m}$. Calculate the time period and frequency of the car.

A CD-ROM drive spins the disc at $1600 \mathrm{rpm}$, Find the time period of the disc.

An object moving in a circular motion has a centripetal acceleration of $20 {\mathrm{ms}}^{-2}$. If the radius of the motion is $0.5 \mathrm{m}$, calculate the time period and frequency of the motion.