A solid sphere of mass \(M\) and radius \(R\) is in pure rolling with angular speed on a horizontal plane as shown.
The magnitude of the angular momentum of the sphere about the origin \(O\) is:
1.
2.
3.
4.
A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m are attached gently to the opposite ends of the diameter of the ring, the ring will then rotate with an angular velocity:
1. | \(\frac{\omega(M-2 m)}{M+2 m} \) | 2. | \(\frac{\omega M}{M+2 m} \) |
3. | \(\frac{\omega(M+2 m)}{M} \) | 4. | \(\frac{\omega M}{M+m}\) |
A thin uniform circular disc of mass \(M\) and radius \(R\) is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with an angular velocity . Another disc of the same dimensions but of mass \(\frac{1}{4}M\) is placed gently on the first disc co-axially. The angular velocity of the system will be:
1. | 2. | ||
3. | 4. |
A boy is standing on a disc rotating about the vertical axis passing through its centre. He pulls his arms towards himself, reducing his moment of inertia by a factor of m. The new angular speed of the disc becomes double its initial value. If the moment of inertia of the boy is I0 , then the moment of inertia of the disc will be:
1.
2.
3.
4.
Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D has a 2 kg mass, 0.2 m radius, and an initial angular velocity of 50 rad s. Disc D has 4 kg mass, 0.1 m radius, and initial angular velocity of 200 rad s. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad.s) of the system will be:
1. 60
2. 100
3. 120
4. 40
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along:
1. | a line perpendicular to the plane of rotation |
2. | the line making an angle of \(45^\circ\) to the plane of rotation |
3. | the radius |
4. | the tangent to the orbit |
A rod is falling down with constant velocity \(V_0\) as shown. It makes contact with hinge A and rotates around it. The angular velocity of the rod just after the moment when it comes in contact with hinge A is:
1. | \(2 \mathrm{V}_0 / 3 \mathrm{L} \) | 2. | \(3 \mathrm{V}_0 / 2 \mathrm{L} \) |
3. | \(\mathrm{V}_0 / \mathrm{L} \) | 4. | \(2 \mathrm{V}_0 / 5 \mathrm{L}\) |
If the radius of the earth is suddenly contracted to half of its present value, then the duration of the day will be of:
1. | 6 hours | 2. | 12 hours |
3. | 18 hours | 4. | 24 hours |
The law of conservation of angular momentum is valid when:
1. | The net force is zero and the net torque is non-zero | 2. | The net force is non-zero and the net torque is non zero |
3. | Net force may or may not be zero and net torque is zero | 4. | Both force and torque must be zero |
Which of the following will not be affected if the radius of the sphere is increased while keeping mass constant?
1. | Moment of inertia | 2. | Angular momentum |
3. | Angular velocity | 4. | Rotational kinetic energy |