Angular Impulse

Q. a force of \overrightarrow F=i+3J+6k is acting at a point r= 2i-6j-12k. the value of α for which the angular momentum is conserved

Q. A force F = ai +3j+6k is acting at a point72i-61-12k. Find the value of a for whichangular momentum about origin is conserved.(1) 0(2) 1(3) -1(4) 2

Q. A uniform disk (m = 2 kg, r = 50 cm) is rotating at an angular speed 480 rpm. A second disk (m = 1 kg, r = 160 cm) is rotating at speed 360 rpm. Now first disk is dropped gently on second disk & they eventually rotate together about common axis. Find final angular velocity in rad/s.

1. 12.6 $\pi$
2. 11.2$\pi$
3. 22.4 $\pi$
4. 6.4 $\pi$

Q.

There are two point masses each of mass m are at the ends of a rod of mass m. The rod is released. What will be the angular speed when it becomes vertical?

1. 

2. 

3. 

4. 

Q. A force $\overrightarrow{F}=\alpha \hat{i}+3\hat{j}+6\hat{k}$ is acting at a point $\overrightarrow{r}=2\hat{i}-6\hat{j}-12\hat{k}$. The value of $\alpha$ for which angular momentum about origin is conserved is

1. 1
2. -1
3. 2
4. \N

Q. Two small balls A and B, each of mass m, are joined rigidly to the ends of a light rod of length L (figure 10-E10). The system translates on a frictionless horizontal surface with a velocity ${\nu }_0$ in a direction perpendicular to the rod. A particle P of mass m kept at rest on the surface sticks to the ball A as the ball collides with it. Find
(a) the linear speeds of the balls A and B after the collision, (b) the velocity of the centre of mass C of the system A + B + P and (c) the angular speed of the system about C after the collision.

Figure

Q. A circular wooden loop of mass $m$ and radius $R$ rests flat on a horizontal frictionless surface. A bullet, also of mass $m$, and moving with a velocity $V$, strikes the loop at the bottommost point and gets embedded in it. The thickness of the loop is much smaller than $R$. The angular velocity with which the system rotates just after the bullet strikes the loop is

1. $\frac{V}{4R}$
2. $\frac{V}{3R}$
3. $\frac{2V}{3R}$
4. $\frac{3V}{4R}$

Q. A uniform disc of mass $m$ and radius $R$ is placed on a smooth horizontal surface. An impulse $I$ is given horizontally to the sphere at height $h=\frac{3R}{5}$ above the centre line. Then which of the following option(s) is correct?

1. The minimum time after which the highest point touches the ground is $\frac{\pi Rm}{2I}$
2. The minimum time after which the highest point touches the ground is $\frac{5\pi Rm}{6I}$
3. The displacement of the COM during this interval is $\frac{5\pi R}{6}$
4. The displacement of the COM during this interval is $\frac{\pi R}{2}$

Q. A pulley is rotated about its axis by a force $F=(20t-5t^2)\text{N}$ (where $t$ is measured in seconds) applied tangentially. Find the magnitude of angular impulse [in $\text{Nm-s}$] on the pulley in the initial $2\text{seconds}$. Given radius of pulley $=0.5\text{m}$.

1. $10/3$
2. $20/3$
3. $40/3$
4. zero

Q. Figure shows a small body of mass m placed over a larger mass M whose surface is horizontal near the smaller mass and gradually curves to become vertical. The smaller mass is pushed on the longer one at a speed v and$$\begin{gathered} v_m=u=a_{2}t \\ =\frac{mg\sin \alpha \cos \alpha }{\mathrm{M}+m}\sqrt{\frac{2h}{a\sin \alpha }}={\left[\frac{2m^2{g}^{2}h{\sin }^2\alpha c{o}^2\alpha }{(\mathrm{M}+m{)}^{2}a\sin \alpha }\right]}^{1/2} \end{gathered}$$ the system is left to itself. Assume that all the surface are frictionless. (a) Find the speed of the larger block when the smaller block is sliding on the vertical part. (b) Find the speed of the smaller mass when it breaks off the larger mass at height h. (c) Find the maximum height (from the ground) that the smaller mass ascends. (d) Show that the smaller mass will again land on the bigger one. Find the distance traversed by the bigger block during the time when the smaller block was in its flight under gravity.
Figure

Q. Find the angular impulse applied to the particle in the 4 sec.

1. $10{\text{kg-m}}^2/\text{sec}$
2. $40{\text{kg-m}}^2/\text{sec}$
3. $20{\text{kg-m}}^2/\text{sec}$
4. $5{\text{kg-m}}^2/\text{sec}$

Q. A pulley is rotated about its axis by a force $F=(20t-5t^2)\text{N}$ (where $t$ is measured in seconds) applied tangentially. Find the magnitude of angular impulse [in $\text{Nm-s}$] on the pulley in the initial $2\text{seconds}$. Given radius of pulley $=0.5\text{m}$.

1. $10/3$
2. $20/3$
3. $40/3$
4. zero

Q. Two small balls A and B, each of mass m, are attached rigidly to the ends of a light rod of length d. The structure rotates about the perpendicular bisector of the rod at an angular speed $\omega$. The angular momentum of the system about the axis of rotation is .

1. $m\omega d^2$
2. $2m\omega d^2$
3. $\frac{1}{2}m\omega d^2$
4. $\frac{1}{4}m\omega d^2$

Q. Why the angular momentum of the body cannot be zero if the net external force is not equal to zero?