Kinematics of Rotation

Assertion: The angular velocity of all the points on the rigid body as seen from any other point on it is the same.

Reason: The distance between any 2 points on the rigid body remains constant. 

The angular velocity of a scooter tyre of diameter $6$ inches rotates $6$ times a second is:

Calculate the angular velocity of a particle moving along the straight line given by θ = 3t³ + 6t + 2 when t = 5s

What is angular velocity ?

Find the angular velocity of a body rotating with an acceleration of $2 \mathrm{rev} {\mathrm{s}}^{-2}$ as it completes the $5^{\mathrm{th}}$ revolution after the start.

A body rotates about a fixed axis with an angular acceleration of $1 \mathrm{rad} {\mathrm{s}}^{-2}$. Through what angle does it rotate during the time in which its angular velocity increases from $5 \mathrm{rad} {\mathrm{s}}^{-1}$ to $15 \mathrm{rad} {\mathrm{s}}^{-1}$?

Defined pure rotational motion?

Define angular acceleration and translational acceleration.

The oxygen molecule has a mass of $5.30\times {10}^{-26} \mathrm{kg}$ and a moment of inertia of $1.94\times {10}^{-46} {\mathrm{kgm}}^2$ about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is $500 \mathrm{m}/\mathrm{s}$ and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

Two particles of equal mass $\text{'}m\text{'}$go around a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each partial
with respect to their centre of mass is :

A mass $\text{'}m\text{'}$ supported by a massless string wound around a uniform solid cylinder of mass $m$ and radius $R.$ If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

If a spherical ball rolls on a table without slipping, the fraction of its total energy associated with rotation is :-

The fraction of total energy of spherical shell is translatory kinetic energy motion is,

When a ceiling fan is switched off its angular velocity reduces to $50\%$ while it makes $36$ rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation):-

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is

A rectangular plate of mass $20 \mathrm{kg}$ is suspended from two pins $\mathrm{A}$and$\mathrm{B}$as shown in the figure. If the pin $\mathrm{B}$ is suddenly removed, determine the angular acceleration (in $\mathrm{rad} {\mathrm{s}}^{-2}$ ) of the plate

A frictionless hinge supports a bar of mass m and length L in the vertical position. The hinge is a sort of pivot that can offer no resistance to the bar against an applied moment. However, the reaction is what it offers. If the bar is released, find the reaction at the support, when the bar comes down to the horizontal position.

A couple causes

A disc rotating about its axis with angular speed $\omega {}_0$ is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is $R$. Let $v_A, v_B$ and $v_C$ be the magnitudes of linear velocities of the points $A, B$ and $C$ on the disk as shown. Then,

A wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of ${15}^o$ in time t sec. The increase in angle through which it rotates in the next 2t sec is