Embibe Experts Solutions for Chapter: Rotational Motion, Exercise 1: Exercise 1

The velocity of the centre of mass of a solid sphere of radius $R$ rotating with angular velocity $\omega$ about an axis passing through its centre of mass is

Two rings of same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is, (Mass of the ring$=m$, radius$=r$.)

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along,

A body is rotating with angular momentum $L.$ If $I$ is its moment of inertia about the axis of rotation, its kinetic energy of rotation is

A solid cube of wood of side $2a$ and mass $M$ is resting on a horizontal surface as shown in the figure. The cube is free to rotate about a fixed axis $AB.$ A bullet of mass $m(<<M)$ and speed $v$ is shot horizontally at the face opposite to $ABCD$ at a height of $\frac{4a}{3}$ from the surface to impart the cube and angular speed $\omega .$ It strikes the face and embeds in the cube. Then $\omega$ is close to (note: the moment of inertia of the cube about an axis perpendicular to the face and passing through the center of mass is $\frac{2M{a}^2}{3}$.)

A horizontal disk of moment of inertia $4.25 \mathrm{kg} {\mathrm{m}}^2$ with respect to its axis of symmetry is spinning counter-clockwise at $15$ revolutions per second about its axis, as viewed from above. A second disk of moment of inertia $1.80 \mathrm{kg} {\mathrm{m}}^2$ with respect to its axis of symmetry is spinning clockwise at $25$ revolutions per second as viewed from above about the same axis and is dropped on top of the first disk. The two disks stick together and rotate as one about their axis of symmetry. The new angular velocity of the system as viewed from above is close to-

A particle is in a uniform circular motion in a horizontal plane. Its angular momentum is constant when the origin is taken at 

What remains constant in the field of central force?