Conservation of Angular Momentum

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:

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is $K$. The child stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is

A solid sphere is rotating in free space. If the radius of sphere is increased keeping mass same which one of the following will not be affected?

A uniform rod $\mathrm{AB}$ of length$L$ and mass $M$is lying on a smooth table. A small particle of mass $m$ strikes the rod with velocity $v_0$ at point $C$ at a distance $x$from the centre $O$. The particle comes to rest after collision. The value of $x$, so that the point $\mathrm{A}$of the rod remains stationary just after the collision, is$L/n$, then find $n$.

Relation between Torque and angular momentum is similar to the relation between

A uniform rod $\mathrm{AB}$ of length$L$ and mass $M$is lying on a smooth table. A small particle of mass $m$ strikes the rod with velocity $v_0$ at point $C$ at a distance $x$from the centre $O$. The particle comes to rest after collision. If the value of $x$, so that the point $\mathrm{A}$of the rod remains stationary just after the collision, is$L/n$, then find $n$.

Relation between Torque and angular momentum is similar to the relation between

As shown in the figure, two balls of same mass $m$ are situated at the centre of a tube of mass $M$ and are rotating with a uniform angular velocity ${\omega }_0.$ If the balls suddenly come to end of the tube the resultant angular velocity will be :

Under the influence of the Coulomb field of charge $+Q,$ a charge $-q$ is moving around it in an elliptical orbit. Find out the correct statement.

A disc is free to rotate about a smooth horizontal axis passing through its centre of mass. A particle is fixed at the top of the disc. A slight push is given to the disc and it starts rotating. During the process

A time varying torque $\left(4t\right) \mathrm{N} \mathrm{m}$ is applied on an object about a pivot. Change in angular momentum of body till time $t=3\mathrm{ }\mathrm{s}$ is:

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

A uniform rod of mass $M$ and length $a$ lies on a smooth horizontal plane. A particle of mass $m$ moving at a speed $v$ perpendicular to the length of the rod strikes it at a distance of $\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ from the centre and stops after the collision. The angular velocity of the rod about its centre just after the collision is

A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is

$g$ is the acceleration due to gravity and $K$ is the rotational kinetic energy of the earth. If the earth's radius increases by $2\%$ keeping mass constant, then the value of decrement in $g$ and $K$ is $\dots \dots \%$

In the figure half of the meter scale is made of wood while the other half is of steel. In figure $\left(a\right)$ the wooden part is pivoted at $O$. A force $F$ is applied at the end of the steel part. In figure $\left(b\right)$ the steel part is pivoted at $O^{\text{'}}$ and the same force is applied at the wooden end.

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 rigid spherical body is spinning about an axis without any external torque. Due to change in temperature, the volume increases by $3\%.$ The angular speed will approximately

If net torque acting on a system is zero, then

A uniform rod of mass $m$ and length $l$ can rotate freely on a smooth horizontal plane about a vertical axis hinged at point $\mathrm{H}$. A point mass having the same mass $m$ coming with an initial speed u perpendicular to the rod, strikes the rod and sticks to it at a distance of $\frac{3l}{4}$ from hinge point. The angular velocity of the rod just after collision is $\frac{36u}{nl}$. Find the value of $n$.