Angular Momentum

Q. A flat surface of a thin uniform disk $A$ of radius $R$ is glued to a horizontal table. Another thin uniform disk $B$ of mass $M$ and with the same radius $R$ rolls without slipping on the circumference of $A$, as shown in the figure. A flat surface of $B$ also lies on the plane of the table. The center of mass of $B$ has fixed angular speed $\omega$ about the vertical axis passing through the center of $A$. The angular momentum of $B$ is $nM\omega R^2$ with respect to the center of $A$. Which of the following is the value of $n$?

1. $2$
2. $\frac{9}{2}$
3. $5$
4. $\frac{7}{2}$

Q.

A homogenous rod of length ℓ = ηx and mass, M is lying on a smooth horizontal floor. A bullet of mass 'm' hits the rod at a distance 'x' from the middle of the rod at a velocity $v_0$ perpendicular to the rod and comes to rest after collision. If the velocity of the farther end of the rod just after the impact is in the opposite direction of $v_0$, then:

1. η> 3

2. η< 3

3. η> 6

4. η< 6

Q.

In a horizontal smooth plane. If a particle sticks after collision to the rod, find the final angular velocity .

1. 

2. 

3. 

4. None of these

Q.

A uniform solid sphere of radius R, rolling without sliding on a horizontal surface with an angular velocity ${\omega }_0$, meets a rough inclined plane of inclination $\theta ={60}^{\circ }$.The sphere starts pure rolling up the plane with an angular velocity $\omega$ . Find the value of $\omega$.

1. 

2. 

3. 

4. 

Q.

In the shown figure a mass m slides down the frictionless surface from height h and collides with a uniform vertical rod of length L and mass M. After a collision, mass m sticks to the rod. The rod is free to rotate in a vertical plane about a fixed axis through O. Find the maximum angular deflection of the rod from its initial position

1. None of these

2. 

3. 

4. 

Q.

Two uniform rods AB and BC of masses 1 kg and 2 kg respectively having lengths 2 m and 1 m respectively are joined to each other at B. They can rotate freely about B without any friction. The assembly is kept on a smooth horizontal surface as shown in figure.
A horizontal impulse P = 10 Ns is applied on the rod
AB at a distance 0.5 m from point B perpendicular to the rod

Angular momentum of rod BC about centre of rod BC just after application of impulse is

1. 

2. 6 kg - m²/s

3. 

4. 

Q.

A uniform solid sphere of mass m and radius R is placed on a horizontal surface. A horizontal linear impulse P is applied at a height $\frac{R}{2}$ above its center. Find the velocity of center of mass and angular velocity of sphere just after the impulse is applied.

1. None of these

2. 

3. 

4. 

Q. Moment of inertia of uniform rod of mass 'M' and length 'L' about an axis through its centre and perpendicular to its length is given by $\frac{M{L}^2}{12}$. Now consider one such rod pivoted at its centre, free to rotate in a vertical plane. The rod is at rest in the vertical position. A bullet of mass 'M'moving horizontally at a speed 'v' strikes and embedded in one end of the rod. The angular velocity of the rod just after the collision will be

1. 
2. 
3. 
4. 

Q.

A disc of mass 'M' and radius 'R' is rolling with an angular speed of $\omega$ rad/s on a horizontal plane as shown in the figure. The magnitude of angular momentum of the disc about the origin O is

1. 
2. 
3. 
4. 

Q. Two discs of moment of inertia $I_1$ and $I_2$ and angular speeds ${\omega }_1$ and ${\omega }_2$ are rotating along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate together along the same axis the rotational KE of system will be

1. 
2. 
3. 
4. None of these