Angular Impulse and Angular Momentum

Q.

State the law of simple pendulum.

Q. A simple pendulum of length of 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of $5\frac{m}{s}.$ The net force on bob at the mean position is

1. Zero

2. 2.5 N

3. 5 N

4. 25 N

Q.

What is K in Pendulum?

Q.

A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force P is applied at a distance of $\frac{2L}{3}$ from the hinge so that the rod swings to the right. The horizontal reaction at the hinge is

1. -P

2. 0

3. $\frac{P}{3}$

4. $\frac{2P}{3}$

Q. A cord of negligible mass is wrapped around the outer surface of a 5 kg disk of radius 0.5 m as shown. If the disk is released from rest, the angular velocity of the disk (in rad/s) after 3 seconds is
(acceleration due to gravity, g = 10 m/s${}^2$)

1. 30
2. 40
3. 60
4. 120

Q.

A pin jointed uniform rigid rod of weight W and length L is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is

1. Zero

2. $\frac{W}{4}$

3. $\frac{W}{2}$

4. W

Q. A 1 kg mass of clay, moving with a velocity of 10$\frac{m}{s}$, strikes a stationary wheel and sticks to it. The solid wheel has a mass of 20 kg and a radius of 1 m. Assuming that the wheel is set into pure rolling motion, the angular velocity of the wheel immediately after the impact is approximately

1. Zero
2. $\frac{1}{3}rad/s$
   
3. $\sqrt{\frac{10}{3}}rad/s$
4. $\frac{10}{3}rad/s$

Q. A right circular cylinder of radius r and weight W is suspended by a cord that is wound around its surface. If the cylinder is allowed to fall, find the tension in the cord.

1. $\frac{W}{3}$
2. $\frac{2W}{3}$
3. $\frac{W}{2}$
4. W

Q. A system of particles in motion has mass center G as shown in the figure. The particle i has mass $m_i$ and its position with respect to a fixed point O is given by the position vector ${\rho }_i$. The position of the particle with respect to g is given by the vector ${\rho }_i$. The time rate of change of the angular momentum of the system of particles about G is (The quantity $\ddot{{\rho }_i}$ indicates second derivative of ${\rho }_i$ with respect to time and likewise for $r_i$

1. ${\Sigma }_i{r}_i\times m_i{\ddot{\rho }}_i$
2. $\Sigma {\rho }_i\times m_i{\ddot{r}}_i$
3. ${\Sigma }_i{r}_i\times m_i{\ddot{r}}_i$
4. ${\Sigma }_i{\rho }_i\times m_i{\ddot{\rho }}_i$

Q. A mass of 2 kg is hung by a string of length 1.5 m as shown in the figure. The mass revolves in a horizontal circular path at 50 revolutions per minute.


The tension in the string in Newtons is

1. $25\pi /3$
2. $25{\pi }^2/3$
3. $50\pi /3$
4. $50{\pi }^2/3$

Q.

How knowledgeable are you about the simple pendulum?

Q. One end of a uniform rod of mass and length l is clamped end at a uniform angular velocity $\omega$. the force exerted by the clamp on the rod is

1. $m{\omega }^{2}l$
2. $0$
3. $mg$
4. $\frac{m{\omega }^{2}l}{2}$

Q. A unifonn circular ring of mass M and radius r is rotating with an angular speed $\omega$ about an axis passing through its centre and perpendicular to the plane of the ring. Two identical beads, each of mass m, somehow get attached at two diametrically opposite points. The rotational speed of the ring will become

1. $\frac{\omega M}{M+2m}$
2. $\frac{\omega M}{M+m}$
3. $\frac{2\omega M}{M+2m}$
4. $\omega$