Torque

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

If force $\overrightarrow{F}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}-2\hat{\mathrm{k}}$ acts on a particle having position vector $2\hat{\mathrm{i}}+\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ then, the torque about the origin will be:

A particle of mass M tied to a string of length L is rotating along a circular path with constant speed $\mathrm{\vartheta }$. The torque on the particle is

A force $\overrightarrow{F}=4\hat{\mathrm{i}}-10\hat{\mathrm{j}}$ acts on a body at a point having position vector $\overrightarrow{r}=-5\hat{\mathrm{i}}-3\hat{\mathrm{j}}$ relative to origin of coordinates on the axis of rotation. If the torque acting on the body about origin is $a\hat{\mathrm{k}}$, then find the value of $a$ (in SI units). [Given, $\overrightarrow{F}$ and $\overrightarrow{r}$ are in SI units]

Which relation is not correct of the following?

What are the rotational equivalents for the physical quantity force?

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

What is Angular momentum of a particle?

A horizontal disc is freely rotating about a vertical axis passing through its centre at the rate of $100 \mathrm{rpm}$. A  bob of wax of mass $20 \mathrm{g}$ falls on the disc and sticks to it a distance of $5 \mathrm{cm}$ from the axis. If the moment of inertia of the disc about the given axis $2\times {10}^{-4 } kg m^2$. Find the new frequency of the disc.

What is Torque of force? Discuss the conditions when it is maximum and minimum.

State the law of conservation of Angular momentum.

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 :

A force $\overrightarrow{F}=2\hat{\mathrm{i}}-3\hat{\mathrm{k}}$ acts on a particle at $\overrightarrow{r}=0.5\hat{\mathrm{j}}-2\hat{\mathrm{k}}$. The torque $\overrightarrow{\tau }$ acting on the particle relative to a point with coordinates $(2.0 \mathrm{m}, 0, -3.0 \mathrm{m})$ is

The $747$ Boeing plane is landing at a speed of $70 \mathrm{m}/\mathrm{s}$. Before touching the ground, the wheels are not rotating. How long a skid mark do the wing wheels leave?

When a tree is cut, the cut is made on the side facing the direction in which the tree is required to fall. Why?

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:

If net external torque, about a point, acting on the system is zero, then we can surely say

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