Angular Analogue of Linear Momentum

Q. The angular momentum of a particle rotating with a central force is constant due to

1. constant linear momentum
2. zero torque
3. constant torque
4. constant force

Q. A solid cylinder of mass 2 kg and radius 0.2 mis rotating about its own axis without friction with angular velocity 3 rad/s. A particle of mass 0.5 kg moving with a velocity 5 m/s strikes the cylinder and sticks to it as shown in figure below. The angular momentum of the cylinder before collision will be

1. 0.12 J-s
2. 12 J-s
3. 1.2 J-s
4. 1.1.2 J-s

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

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

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 m is projected with velocity v making an angle of ${45}^{\circ }$ with the horizontal. Themagnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height is (where g = acceleration due to gravity)

1. $Zero$

2. $\frac{m{v}^2}{2g}$

3. $\frac{m{v}^3}{\left(4\sqrt{2}g\right)}$

4. $\frac{m{v}^3}{\left(\sqrt{2}g\right)}$

Q. A child with mass $m$ is standing at the edge of a merry-go-round (A large uniform disc which rotates in horizontal plane about a fixed vertical axis in parks) with moment of inertia $I$, radius $R$, and initial angular velocity as shown in figure.The child jumps off the edge of the merry-go-round with a velocity $v$ with respect to the ground in direction tangent to periphery of the disc as shown.The new angular velocity of the merry-go-round is:

1. $\sqrt{\frac{I{\omega }^2-m{v}^2}{I}}$
2. $\sqrt{\frac{(I+m{R}^2){\omega }^2-m{v}^2}{I}}$
3. $\frac{I\omega -mvR}{I}$
4. $\frac{(I+m{R}^2)\omega -mvR}{I}$

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. Which of the following quantities will remain unchanged for both objects?

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

Q.

A particle is projected at time $t$ = 0 from a point $P$ with a speed $v_0$ at an angle of ${45}^{\circ }$ to the horizontal. Find the magnitude and the direction of the angular momentum of the particle about the point $P$ at time $t$ = $\frac{v_0}{g}$

1. $\frac{m{v}_0^2}{2\sqrt{2}g}(-\hat{k})$

2. $\frac{m{v}_0^3}{2\sqrt{2}g}(-\hat{k})$

3. $\frac{m{v}_0^2}{2\sqrt{2}g}\left(\hat{k}\right)$

4. $\frac{m{v}_0^3}{2\sqrt{2}g}\left(\hat{k}\right)$

Q.

A particle '$m$' starts with zero velocity along a line $y$ = $4d$. (Where $d$ is a constant). The position of particle '$m$' varies as $x$ = $Asin\omega t$. At $\omega t$ = $\frac{\pi }{2}$, its angular momentum with respect to the origin is?

1. $mA\omega d$

2. $\frac{m\omega d}{A}$

3. $\frac{mAd}{\omega }$

4. zero

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 particle is projected at time t =0 from a point P with a speed $v_0$ at an angle of 45${}^{\circ }$ to the horizontal. Find the magnitude and the direction of the angular momentum of the particle about the point P at time t =$\frac{v_0}{g}$.

1. $\frac{m{v}_0^3}{2\sqrt{2}g}\hat{j}$

2. $\frac{m{v}_0^3}{2\sqrt{2}g}\widehat{(}-j)$

3. $\frac{m{v}_0^3}{\sqrt{2}g}\hat{j}$

4. $\frac{2m{v}_0^3}{3}\widehat{(}-j)$

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

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

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

Q. The critical velocity of the satellite is maximum in ______.

1. MEO
2. HEO
3. LEO
4. Polar orbit

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 ball 'A' of mass 'm' is attached rigidly to the end of a light rod of length 'd'. The structure rotates about an axis perpendicular to the rod and passing through its other end with an angular velocity '$\omega$'. Calculate the angular momentum of the system about this axis?

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

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. 0.003083 $kg{m}^2$

2. 0.004083 $kg{m}^2$

3. 0.002083 $kg{m}^2$

4. 0.001083 $kg{m}^2$