Angular Momentum and its Conservation

A planet of mass $m$ is in an elliptical orbit about the sun $\left(m<<M_{\text{sun}}\right)$ with an orbital period $T$. If $A$ be the area of orbit, then its angular momentum would be

The angular momentum of a particle with respect to the origin will not be zero, if

Two persons stand at the edges of a rotating circular platform at diametrically opposite points. If they start moving towards each other at uniform velocity, then its

Consider a particle of unit mass being thrown with an initial velocity $v_0$ making an angle $\varphi$ with the horizontal ground. What is the magnitude of the angular momentum of the particle about the point of projection at a time $t$ after its projection while it is in fight?

Particles of mass $m_1$ and $m_2$ initially sitting at the same position, start moving simultaneously at $t=0$ with velocities $v_1$ and $v_2$, respectively. After a time $t=t_0$ the angular momentum of the particle of mass ${\mathrm{m}}_2$ with respect to the particle of mass $m_1$ is

A planet of mass $m$ moves in an elliptical path around the Sun (which is at one of the foci of the ellipse), so that its maximum and minimum distances from the Sun are $r_{\max }$ and $r_{min }$, respectively. Taking the gravitational constant to be $G$ and the mass of the Sun to be $M_s$, what is the angular momentum of the planet relative to the centre of the Sun?

A bob of mass m attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega$ rad/s about the vertical. About the point of suspension :

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

Given $\overrightarrow{r}=4\widehat{\mathrm{j}}$ and $\overrightarrow{p}=2\widehat{\mathrm{i}}+3\widehat{\mathrm{j}}+\widehat{\mathrm{k}}$ . The angular momentum is

Which of the following physical quantity is represented by the product of the moment of inertia and angular velocity? 

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 ball of mass $160 \mathrm{g}$ is thrown up at an angle of $60°$ to the horizontal at a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly $\left(\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

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 $n$.

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 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 $n$.

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 particle of mass $10 \mathrm{g}$ starts from rest at $\mathrm{t}=0 \mathrm{s}$ from a point $(0\mathrm{m}, 4\mathrm{m})$ and gets accelerated at $0.5 \mathrm{m}/{\mathrm{s}}^2$ along $x-\sqrt{3}y+4\sqrt{3}=0$ in $XY$ plane. The angular momentum of the particle about the origin (in SI units ) at $\mathrm{t}=2 \mathrm{s}$ is

Assertion : The net momentum of a system of two moving particles is zero. Then at a particular instant of time, the net angular momentum of system of given two particle is same about any point.

Reason : If net momentum of a system of two moving particle is zero, then angular momentum of system of given two particles is zero about any point.