Angular Velocity

Q.

The phase difference between displacement and acceleration of a particle performing SHM is?

Q. The angular speed of a flywheel making $120\text{revolutions /minute}$ is

1. $4{\pi }^2\text{rad/s}$
2. $2{\pi }^2\text{rad/s}$
3. $\pi \text{rad/s}$
4. $4\pi \text{rad/s}$

Q.

Calculate the angular speed of the second hand and hour hand of the clock?

Q.

The angular velocity of a particle rotating in a circular orbit 100 times per minute is

1. 1.66 rad/s

2. 10.47 rad/s

3. 60 deg/s

4. 10.47 deg/s

Q. A body rotating with a uniform angular acceleration covers $100\pi$ radians in first 5 s after the start. Find its angular speed at the end of 5 s.

Q. A particle P is moving in a circle of radius 'a' with a uniform speed v . C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and B are in the ratio

1. 1 : 1
2. 2 : 1
3. 4 : 1
4. 1 : 2

Q. A uniform rod of length $L$ is free to rotate in a vertical plane about a fixed horizontal axis through $B$. The rod begins rotating from rest from its unstable equilibrium position. When it has turned through an angle $\theta$, its angular velocity $\omega$ is given as:

1. $\sqrt{\frac{6g}{L}}\sin \theta$
2. $\sqrt{\frac{6g}{L}}\sin \frac{\theta }{2}$
3. $\sqrt{\frac{6g}{L}}\cos \frac{\theta }{2}$
4. $\sqrt{\frac{6g}{L}}\cos \theta$

Q. A rigid body is in pure rotation, about a fixed axis. Then which of the following statement(s) is/are true ?

1. You can find two points in the body in a plane perpendicular to the axis of rotation having same velocity.
2. You can find two points in the body in a plane perpendicular to the axis of rotation having the same acceleration
3. Speed of all the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation is the same
4. Angular speed of the body is the same as seen from any point on the body.

Q.

In 1.0 s, a particle goes from point A to point B, moving in a semicircle of radius 1.0 m (see figure). The magnitude of the average velocity is

1. 3.14 m/s

2. 2.0 m/s

3. 1.0 m/s

4. Zero

Q. If angular velocity of a disc depends an angle rotated $\theta$ as $\omega ={\theta }^2+2\theta$, then its angular acceleration $\alpha$ at $\theta =1\text{rad}$ is

1. $8{\text{rad/sec}}^2$
2. $10{\text{rad/sec}}^2$
3. $12{\text{rad/sec}}^2$
4. None

Q.

A satellite in a circular orbit of radius $R$ has a period of $4h$. Another satellite with an orbital radius of $3R$ around the same planet will have a period

(in hours)

1. $16$

2. $4$

3. $4\sqrt{27}$

4. $4\sqrt{8}$

Q. The angular velocity of a particle moving in a circle of radius $50\text{cm}$ is increased in $5\text{min}$ from $100$ revolutions per minute to $400$ revolutions per minute.
Find its angular acceleration in ${\text{rad/s}}^2$

Q. A particle is moving with constant speed in a circular path. Find the ratio of average velocity from $\theta =0$ to $\theta =\frac{\pi }{2}$ to its instantaneous velocity at $\theta =\frac{\pi }{2}$.

1. $\frac{\sqrt{2}}{\pi }$
2. $\frac{\sqrt{2}}{2\pi }$
3. $\frac{2\sqrt{2}}{\pi }$
4. $\frac{2\sqrt{2}}{3\pi }$

Q.

How to calculate the mass of the sun?

Q.

A ballet dancer spins with 24 $rev{s}^{-1}$ with her arms stretched out when the moment of inertia about the axis of rotation is 1. Calculate the new rate of spin, if the moment of inertia about the same axis is 0.61.

1. 10 rev/s

2. 20 rev/s

3. 30 rev/s

4. 40 rev/s

Q. The orbital velocity of an artificial satellite in a circular orbit just above the earth’s surface is $v$. For a satellite orbiting at an altitude of half of the earth’s radius, the orbital velocity will be

1. $\frac{3}{2}v$
2. 
   $\sqrt{\frac{2}{3}}v$
3. $\sqrt{\frac{3}{2}}v$
4. $\frac{2}{3}v$

Q. What is the ratio of the angular velocity of the hour hand of a watch to the angular velocity of Earth's rotation about its axis?

1. $2:1$
2. $4:1$
3. $5:1$
4. $3:1$

Q. If the equation for the angular displacement of a particle moving on a circular path is given by $\theta =2t^3+0.5$, where $\theta$ is in radians and $t$ in seconds, then the angular velocity of the particle at $2\text{s}$ is

1. $8\text{rad/s}$
2. $12\text{rad/s}$
3. $24\text{rad/s}$
4. $36\text{rad/s}$

Q. Two coaxial discs, having moments of inertia $I_1$ and $I_1/2$ are rotating with respective angular velocities ${\omega }_1$ and ${\omega }_1/2$, about their common axis. They are brought in contact with each other, and thereafter they rotate with a common angular velocity. If $E_f$ and $E_i$, are the final and initial total energies, then $(E_f-E_i)$ is

1. $-\frac{I_1{\omega }_1^2}{24}$
2. $-\frac{I_1{\omega }_1^2}{12}$
3. $\frac{3}{8}{I}_1{\omega }_1^2$
4. $\frac{I_1{\omega }_1^2}{6}$

Q. The angular velocity of earth about its axis of rotation is

1. $\frac{2\pi }{(60\times 60\times 24)}\text{rad/sec}$
2. $\frac{2\pi }{(60\times 60)}\text{rad/sec}$
3. $\frac{2\pi }{(365\times 24\times 60\times 60)}\text{rad/sec}$
4. $\frac{2\pi }{60}\text{rad/sec}$

Q. A magnetising field of $5000\text{A/m}$ produces a magnetic flux of $5\times {10}^{-5}\text{wb}$ in an iron rod is $0.5{\text{cm}}^2$, then the permeability of the rod will be (in $\text{H/m}$)

1. $2\times {10}^{-4}$
2. $1\times {10}^{-3}$
3. $4\times {10}^{-6}$
4. $3\times {10}^{-5}$

Q. The angular velocity of a particle is given by $\omega =1.5t-3t^2+2$, the time when its angular acceleration ceases to exist will be -

1. $25\text{sec}$
2. $0.25\text{sec}$
3. $12\text{sec}$
4. $1.2\text{sec}$

Q. The ratio of angular speeds of second hand and minute hand of a watch is

1. $60:1$
2. $12:1$
3. $1:60$
4. $1:12$

Q. If $\theta$ depends on time $t$ as $\theta =2t^2+3$, find the average angular velocity at the end of $3\text{sec}$ and instantaneous angular velocity at $t=3\text{sec}$ (in $rad/s$)

1. $6,12$
2. $6,6$
3. $8,12$
4. $12,4$

Q.

A homogeneous rod AB of length L and mass M is pivoted at the centre O in such a way that it can rotate freely in the vertical plane. The rod is initially in the horizontal position. An insect S of the same mass M falls vertically with speed V on the point C mid-way between O and B. The initial angular velocity $\omega$ in terms of V and L is

1. 

2. 

3. 

4. 

Q. A motor drives a body along a straight line with a constant force. The power P developed by the motor must vary with time t as

1. 
2. 
3. 
4. 

Q.

A dumb-bell consists of two identical small balls of mass $\frac{1}{2}$ kg each connected to the two ends of a 50 cm long light rod. The dumb-bell is rotating about a fixed axis through the centre of the rod and perpendicular to it at an angular speed of 10 rad/s. An impulsive force of average magnitude 5.0 N acts on one of the masses in the direction of its velocity for 0.10 s. Find the new angular velocity of the system.

Q.

Two masses M and m are connected by a light string going over a pulley of radius r. The pulley is free to rotate about its axis which is kept horizontal. The moment of inertia of the pulley about the axis is I. The system is released from rest. Find the angular momentum of the system when the mass M has descended through a height h. The string does not slip over the pulley.

1. 

2. 

3. 

4. 

Q. A particle starts from the point $(0m,8m)$ and moves with uniform velocity of $3\hat{i}\text{m/s}$. After 5 seconds, the angular velocity of the particle about the origin will be :

1. $\frac{24}{289}\text{rad/s}$
2. $\frac{8}{289}\text{rad/s}$
3. $\frac{3}{8}\text{rad/s}$
4. $\frac{8}{17}\text{rad/s}$

Q. A particle moves parallel to $x-$axis with constant velocity $v$ as shown in the figure. The angular velocity of the particle about the origin $\text{O}$

1. remains constant
2. continuously increases
3. continuously decreases
4. oscillates