Rotational Dynamics

Moment of inertia of a body does not depend upon its

A particle completes 2 revolutions in a circular path of radius 3 cm . The angular displacement of the particle will be (in radian)

For a particle moving in vertical circle, the total energy at different positions along the path [The motion is under gravity]

The angular velocity of seconds hand of a watch will be

Three identical metal balls each of radius ' $r$ ' are placed such that an equilateral triangle is formed when centres of three ball are joined. The centre of mass of the system is located at

A torque of magnitude 4000 N m , acting on a body produces an angular acceleration of $20\mathrm{rad}/s^{2}$. The moment of inertia of the body is

The angular velocity of earth due to its spin motion is

The radius of gyration of a uniform rod of length $L$ about an axis passing through its centre of mass and perpendicular to its length is

A body is rotating about its own axis. Its rotational kinetic energy is ' $x$ ' and its angular momentum is ' $y$ '. Hence its moment of inertia about its own axis is

Two particles having mass ' M ' and ' m ' are moving in a circular path with radius ' R ' and ' r ' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to that of the second particle will be

A solid sphere and thin walled hollow sphere have same mass and same material. Which of them have greater moment of inertia about their diameter?
[ $\mathrm{I}_{\mathrm{h}}=$ moment of inertia of hollow sphere about an axis coinciding with its diameter, $\mathrm{I}_{5}=$ moment of inertia of solid sphere about an axis coinciding with its diameter]

A particle is moving in a circle with uniform speed. It has constant

In case of system of two-particles of different masses, the centre of mass lies

Two objects of masses ' $m_{1}$ ' and ' $m_{2}$ ' are moving in the circles of radii ' $r_{1}$ ' and ' $r_{2}{ }^{\prime}$ respectively. Their respective angular speeds ${ }^{\prime} \omega_{1}{ }^{\prime}$ and ${ }^{\prime} \omega_{2}$ ' are such that they both complete one revolution in the same time ' $t$ '. The ratio of linear speed of ' $m_{2}$ ' to that of ' $m_{1}$ ' is

A body performing uniform circular motion of radius ' $R$ ' has frequency ' $n$ '. Its centripetal acceleration per unit radius is proportional to $(n)^{x}$. The value of $x$ is