Angular Analogue of Linear Momentum

Q. Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:

1. $2:1$
2. $1:2$
3. $\sqrt{2}:1$
4. $1:\sqrt{2}$

Q. The rate of change in angular momentum is

1. Force
2. Energy
3. Torque
4. Impulse

Q. A particle of mass $m$ is projected with velocity $v$ at an angle $\theta$ with the horizontal. Find its angular momentum about the point of projection when it is at the highest point of its trajectory.

1. $\frac{m{v}^2{\sin }^2\theta \cos \theta }{2g}$
2. $\frac{m{v}^3\sin \theta \cos \theta }{g}$
3. $\frac{m{v}^3{\sin }^2\theta \cos \theta }{2g}$
4. $\frac{m{v}^3{\sin }^2\theta \cos \theta }{g}$

Q. Statement - $\text{I}$: $\overrightarrow{L}=I\overrightarrow{\omega }$ is always true for bodies of all shapes.
Statement- $\text{II}$: $\overrightarrow{\tau }=\frac{d\overrightarrow{L}}{dt}$ is always true in inertial frames.

1. Statement $\text{I}$ is true, statement $\text{II}$ is true and statement$\text{II}$ is correct explanation for statement $\text{I}$
2. Statement $\text{I}$ is true, statement $\text{II}$ is true but statement $\text{II}$ is not correct explanation for statement $\text{I}$
3. Statement $\text{I}$ is true but statement $\text{II}$ is false.
4. Statement $\text{I}$ is false but statement $\text{II}$ is true.

Q. 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,

1. angular momentum changes in direction but not in magnitude.
2. angular momentumchanges both in direction and in magnitude.
3. angular momentum is conserved.
4. angular momentum changes in magnitude but not in direction.

Q. A particle of mass $m$ is projected with velocity $v$ at an angle $\theta$ with the horizontal. Find its angular momentum about the point of projection when it is at the highest point of its trajectory.

1. $\frac{m{v}^2{\sin }^2\theta \cos \theta }{2g}$
2. $\frac{m{v}^3\sin \theta \cos \theta }{g}$
3. $\frac{m{v}^3{\sin }^2\theta \cos \theta }{2g}$
4. $\frac{m{v}^3{\sin }^2\theta \cos \theta }{g}$

Q. The position of a particle is given by $\overrightarrow{r}=(\hat{i}+2\hat{j}-\hat{k})$ and momentum $\overrightarrow{P}=(3\hat{i}+4\hat{j}-2\hat{k})$. The direction of angular momentum is perpendicular to

1. X-axis
2. Y-axis
3. Z-axis
4. Line at equal angles to all the three axes

Q.

uniform circular disc of mass 200 g and radius 4.0 cm is rotated about one of its diameter at an angular speed of 10 rad/s. Find the angular momentum about the axis of rotation

1. $4\times {10}^{-4}J-s$

2. $8\times {10}^{-4}J-s$

3. $4\times {10}^{-8}J-s$

4. $8\times {10}^{-8}J-s$

Q. A particle of mass $20\text{gm}$) slides along the frictionless surface. When the particle reaches point $B$, its angular momentum (in ${\text{kg m}}^2/\text{s}$) about $O$ will be


[Take $g=10{\text{m/s}}^2$]

Q. Similar to linear momentum in translatory motion, which of the following can be the magnitude of its rotational analog?

1. Iv
2. $I\omega$
3. $M\omega$
4. $I\alpha$

Q.

A particle of mass 'm' is projected with velocity 'v' making an angle of ${45}^{\circ }$ with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height 'h' is

1. Zero
2. $\frac{m{v}^3}{4g}$
3. $\frac{m{v}^3}{\sqrt{2}g}$
4. $m\sqrt{2g{h}^3}$

Q. The magnitude of the rotational analog of linear momentum is .

1. $I\omega$
2. $M\omega$
3. $I\alpha$
4. $Iv$

Q.

A uniform rod of mass '$m$' and Length '$L$' is rotated about its perpendicular bisector at an angular speed $\omega$. Calculate its angular momentum about its Axis of rotation?

1. $\frac{M{L}^2}{12}\omega$

2. $\frac{2M{L}^2}{12}\omega$

3. $\frac{32M{L}^2}{3}\omega$

4. $\frac{M{L}^2}{24}\omega$

Q.

A cord is wound a round the circumfererence of a wheel of mass 50Kg and diameter 0.3m. The axis of the wheel is horizonatal. A mass of 0.5Kg is attached at the end of the cord. Find the angular acceleration of the wheel?

1. $1.1rad/s^2$

2. $1.2rad/s^2$

3. $1.3rad/s^2$

4. $1.4rad/s^2$

Q. A ring and a disc of same radius and mass are lying on a frictionless surface at rest. The torque of equal magnitude is applied on both for same amount of time. Both the objects are free to rotate about their axis passing through their respective centres and perpendicular to the plane containing them. will be equal for both objects.

1. Angular velocity
2. Angular momentum
3. Moment of Inertia
4. Angular acceleration

Q. A wheel whose moment of inertia is $24kg{m}^2$ starts from rest. Net torque acting on wheel $\tau$ varies with respect to time as shown in the graph. Find the work done by torque in the first 6 seconds.

1. 6.75 J
2. 3.75 J
3. 4.25 J
4. 9.75 J

Q. A mass $m$ is moving with a constant velocity $v$ along a line parallel to $X-$ axis, away from origin. Then, its angular momentum with respect to the origin

1. is zero
2. remains constant
3. goes on increasing
4. goes on decreasing

Q. Similar to linear momentum in translatory motion, which of the following can be the magnitude of its rotational analog?

1. Iv
2. $I\omega$
3. $M\omega$
4. $I\alpha$

Q. A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed $\omega .$ If the angular momentum of the system, calculated about O and P are denoted by ${\overrightarrow{L}}_{O}and{\overrightarrow{L}}_P$ respectively, then

1. ${\overrightarrow{L}}_{O}and{\overrightarrow{L}}_P$ do not vary with time.
2. ${\overrightarrow{L}}_O$ varies with time while ${\overrightarrow{L}}_P$ remains constant.
3. ${\overrightarrow{L}}_O$ remains constant while ${\overrightarrow{L}}_P$ varies with time.
4. ${\overrightarrow{L}}_{O}and{\overrightarrow{L}}_P$ both vary with time.

Q.

A particle of mass 'm' is projected with velocity 'v' making an angle of ${45}^{\circ }$ with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height 'h' is

1. Zero
2. $\frac{m{v}^3}{4g}$
3. $\frac{m{v}^3}{\sqrt{2}g}$
4. $m\sqrt{2g{h}^3}$

Q. A solid body rotates with deceleration about a stationary axis with an angular deceleration $|\alpha |=k\sqrt{\omega }$; where 'k' is a constant and $\omega$ is the angular velocity of the body. If the initial angular velocity is ${\omega }_0$, then mean angular velocity of the body averaged over the whole time of rotation is

1. ${\omega }_0$
2. $\frac{{\omega }_0}{2}$
3. $\frac{{\omega }_0}{3}$
4. $\frac{{\omega }_0}{4}$

Q.

A particle of mass $m$ is moving with constant velocity $v$ parallel to $x$-axis in $x-y$ plane as shown in figure. Calculate its angular momentum with respect to origin at anyinstant '$t$'.

1. mrv

2. mvb

3. $\frac{1}{2}mvb$

4. 2mvb

Q. Find the moment of inertia of a plane rectangular lamina of length 20 cm breadth 10cm and mass 500 g about an axis passing through its centre and perpendicular to its plane.

1. 0.002083 $kg{m}^2$

2. 0.001083 $kg{m}^2$

3. 0.003083 $kg{m}^2$

4. 0.004083 $kg{m}^2$

Q.

Only purely rotating bodies can have angular momentum

A.TRUE

B. FALSE

1. True

2. False

Q.

A particle of mass '$m$' is projected with velocity '$v$' an angle $\theta$ with the horizontal. Find its angular momentum about the point of projection when it is at the highest point of its trajectory?

1. $\frac{m{v}^{3}si{n}^2\theta cos\theta }{2g}$ along positive z Axis

2. $\frac{m{v}^{3}si{n}^2\theta cos\theta }{2g}$along negative z Axis

3. $\frac{m{v}^{3}si{n}^2\theta cos\theta }{g}$along positive z Axis

4. $\frac{m{v}^{3}si{n}^2\theta cos\theta }{2g}$along negative z Axis