Angular Momentum in Case of Rotation about a Fixed Axis

When a body is spinning on its axis in absence of any external torque, then choose the wrong statement

Angular momentum of a system of particles changes when

A ring of mass $M$and radius $R$ is rolling without slipping, the velocity of point$A$ as shown in the figure 

A homogeneous rod AB of length $L$ and mass $M$ is pivoted at the center O in such a way that it can rotate freely in the vertical plane. The rod is initially in the horizontal position. An insect S of the same mass $M$ falls vertically with speed $v$ on the point C mid-way between O and B. Determine the initial angular velocity $\omega$ in terms of $v$ and $L$.

Three uniform rods $AB,BC$ and $CD$ each of mass m and length $l$ are moving together with velocity $v_0$ on a smooth horizontal surface (direction of $v_0$ is perpendicular to length $ABCD$) The roads $AB$ and $CD$ are hinged at $B$ and $C$ respectively so that they can rotate freely about $B$ and $C$. At an instant during the motion, the middle road $BC$ is suddenly fixed on the horizontal surface. Find the time taken for the ends $A$ and $D$ to meet.

A uniform rod of mass $m$ and length / is at rest on smooth horizontal surface. An impulse $P$ is applied to end $B$ as shown in the figure. The point about which the rod can be assumed to be rotating just after the impulse applied is

A cubical block of side $30 \mathrm{cm}$ is moving with velocity $2 \mathrm{m} {\mathrm{s}}^{-1}$ on a smooth horizontal surface. The surface has a bump at a point $O$ as shown in the figure. The angular velocity (in $\mathrm{rad} {\mathrm{s}}^{-1}$) of the block immediately after it hits the bump, is:

An object of mass $2 \mathrm{kg}$ is projected from ground, with initial velocity $40 \mathrm{m} {\mathrm{s}}^{-1}$, making angle $60°$ with the horizontal. Find its angular momentum about the point of projection when the object is at its maximum height. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega .$ Two objects each of mass $m,$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity

An object of mass $2 \mathrm{kg}$ is projected from ground, with initial velocity $40 \mathrm{m} {\mathrm{s}}^{-1}$, making angle $60°$ with the horizontal. Find its angular momentum about the point of projection when the object is at its maximum height. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A uniform circular disc of moment of inertia $2 \mathrm{kg} {\mathrm{m}}^2$ about its axis is rotating with angular speed $4$ $\mathrm{rad} {\mathrm{s}}^{-1}$. Another uniform circular disc of moment of inertia $1 \mathrm{kg} {\mathrm{m}}^2$ about its axis is rotating with angular speed $2 \mathrm{rad} {\mathrm{s}}^{-1}$  in same sense. They are gently brought into contact face to face, coinciding the axis of rotation. The loss of kinetic energy till they attain the common angular velocity, is

A thin circular ring of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis vertical to its plane and passes through center with a constant angular velocity $\omega .$ If two objects each of mass $m$ be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity :-

If the earth were to suddenly contract to ${\frac{1}{\mathrm{n}}}^{\mathrm{th}}$ of its present radius without any change in its mass, then the duration of the new day will be nearly

A solid sphere of mass $m$ and radius $R$ is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis. However it has an angular speed twice that of the sphere. What is the ratio of their kinetic energies of rotation $\left(\frac{E_{\mathrm{sphere}}}{E_{\mathrm{cylinder}}}\right)$ ?

The angular momentum of a particle moving on a circular path with a constant angular velocity is $L$. If the radius of the path is halved while the angular velocity unchanged, The new angular momentum of the particle is

A uniform rod $AB$ of length $l$ and mass $m$ is hanged at point $A$, such that it can rotate in vertical plane, in a car. The car is moving upward with velocity $v_0$ on an inclined plane as shown. If the car comes to halt at once then calculate angular speed with which the rod starts rotating.

A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity ${\mathrm{\omega }}_0$. When the tortoise moves along a chord of the platform with a constant velocity (w.r.t. the platform), Which of the following graphs shows properly the variation of angular velocity of the platform with the time $t$ is-

There is a cubical block with length of its side being $a$. It is moving with a velocity $v$ on a horizontal smooth plane as shown. It hits a ridge at point O. The angular speed of the block after it hits O is

A rotating body has angular momentum $L$. If its frequency of rotation is halved and rotational kinetic energy is doubled, its angular momentum becomes

A man stand on a rotating platform with his arms stretched is holding a $5 \mathrm{kg}$ weight in each hand. The angular speed of the platform is $1.2 \mathrm{rev} {\mathrm{s}}^{-1}$. The moment of inertia of the man together with the platform may be taken to be constant and equal to $6 \mathrm{kg} {\mathrm{m}}^2$. If the man brings his arms close to his chest with the distance of each weight from the axis changing from $100 \mathrm{cm}$ to $20 \mathrm{cm}$, the new angular speed of the platform is