Angular Velocity

Q. Two point P and Q diametrically opposite on a disc of radius $R$ have velocities $v$ and $2v$ as shown in figure. Find the angular speed of Q w.r.t P.

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

Q. A neutron, a proton, an electron and an $\alpha$ particle enter a region of constant magnetic field with equal velocity. The $\overrightarrow{B}$ is along the perpendicularly inward to the plane of the paper. The path followed by each particle is shown in the figure.


The path followed by $\alpha$ particle is represented by:

1. $\text{A}$
2. $\text{B}$
3. $\text{C}$
4. $\text{D}$

Q.

A particle comes round a circle of radius 1 m once. The time taken by it is 10 sec. The average velocity of motion is

1. $0.2\pi m/s$

2. $2\pi m/s$

3. $2m/s$

4. Zero

Q. What is the angular velocity in rad/s of a fly wheel making $300\text{r.p.m}$?

1. $600\pi$
2. $20\pi$
3. $10\pi$
4. $30$

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. Average angular velocity of a body rotating an angle of 3 radians in 0.5 second is

1. 3 rad/s
2. 6 rad/s
3. 12 rad/s
4. 15 rad/s

Q. A particle starts moving from rest at $t=0$ with a tangential acceleration of constant magnitude of $\pi {\text{m/sec}}^2$ along a circle of radius $6\text{m}$. The values of average velocity and average speed during the first $2\sqrt{3}\text{seconds}$ of motion are

1. Average velocity $=2\sqrt{3}\text{m/s}$; Average speed $=\sqrt{3}\text{m/s}$
2. Average velocity $=2\sqrt{3}\text{m/s}$; Average speed $=\sqrt{3}\pi \text{m/s}$
3. Average velocity $=4\sqrt{3}\text{m/s}$; Average speed $=\sqrt{3}\pi \text{m/s}$
4. Average velocity $=\sqrt{3}\text{m/s}$; Average speed $=\sqrt{3}\pi \text{m/s}$

Q. Particle $P$ shown in figure is moving in a circle of radius $R=10cm$ with linear speed $v=2m/s$. Find the angular speed of particle about point $O$

1. $10\text{rad/s}$
2. $20\text{rad/s}$
3. $30\text{rad/s}$
4. $40\text{rad/s}$

Q. A particle is projected at an angle ${60}^{\circ }$ with the horizontal with a speed $10\text{m/sec}$. Find angular velocity about origin when particle touches $X-$ axis again.

1. 1 rad/s
2. 2 rad/s
3. 3 rad/s
4. 4 rad/s

Q. A solid sphere of mass $1\text{kg}$ and radius $2\text{m}$ slips on a rough horizontal plane. At some instant, it has translational velocity $7\text{m/s}$ and angular velocity $\frac{7}{4}\text{rad/s}$ about its centre. The translational velocity in $\text{m/s}$ after the sphere starts pure rolling is
(Enter the nearest integer)

Q.

A particle moves in a circle of radius 20 cm with a linear speed of 10 m/s. It's angular velocity is .

1. 50 rad/sec
2. 10 rad/sec
3. 0.5 rad/sec

Q. Find the average angular speed of the minute hand of a normal clock in $1.5\text{hrs}$.

1. $\frac{\pi }{3600}\text{rad/s}$
2. $\frac{\pi }{1800}\text{rad/s}$
3. $\frac{\pi }{900}\text{rad/s}$
4. $\frac{3\pi }{1800}\text{rad/s}$

Q. A long thin wooden cylindrical pipe of radius R, carrying a uniform surface charge density $\sigma$, is rotating about its axis with an angular velocity $\omega$ that increases slowly with time as $\omega =kt$, $k$ is constant. Which of the statements are correct for region inside the pipe?

1. Magnetic field is uniform and constant with time.
2. Magnetic field is not constant with time.
3. Electric field is zero.
4. Electric field is not zero.

Q. A rod of length $1\text{m}$ rotates in the $xy$ plane about the fixed point $\text{O}$ in the anticlockwise sense, as shown in figure, with angular velocity $\omega =a+bt$ where $a=10{\text{rad s}}^{-1}$ and $b=5{\text{rad s}}^{-2}$. The velocity and acceleration of the point $A$ at $t=0$ is

1. $+10\hat{j}{\text{ms}}^{-1}\text{and}5\hat{j}{\text{ms}}^{-2}$
2. $+10\hat{j}{\text{ms}}^{-1}\text{and}(-100\hat{i}+5\hat{j}){\text{ms}}^{-2}$
3. $-10\hat{j}{\text{ms}}^{-1}\text{and}(100\hat{i}+5\hat{j}){\text{ms}}^{-2}$
4. $+10\hat{j}{\text{ms}}^{-1}\text{and}-5\hat{j}{\text{ms}}^{-2}$

Q. What is the angular velocity in $\text{rad/s}$ of a wheel making $1200$ revolutions in $50$ minutes ?

1. $0.3\pi$
2. $0.5\pi$
3. $0.4\pi$
4. $0.8\pi$

Q. Figure shows two rods p & q moving with a same velocity of $2\text{m/s}$ perpendicular to their length. If angle between the rods is ${106}^{\circ }$, velocity of point of intersection (in$\text{m/s}$) is.

Q. In the figure shown, the instantaneous speed of end $A$ of the rod is $3\text{m/s}$ to the left. Find the angular velocity of the rod at the given instant.

1. $1\text{rad/s}$
2. $2\text{rad/s}$
3. $0.5\text{rad/s}$
4. $0\text{rad/s}$

Q. Two points of a rod move with velocities $30\text{m/s}$ and $10\text{m/s}$ perpendicular to the rod and in the same direction, seperated by a distance $5\text{m}$. Find the angular velocity of the rod.

1. $6\text{rad/s}$
2. $4\text{rad/s}$
3. $2\text{rad/s}$
4. $0\text{rad/s}$

Q. The angular displacement of a particle is given by $\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$, where ${\omega }_0$ and $\alpha$ are constant and ${\omega }_0=1\text{rad/sec},\alpha =1.5{\text{rad/sec}}^2$. The angular velocity $($in $\text{rad/s})$ at time, $t=2\text{sec}$ will be

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

Q. A proton is rotating along a circular path of radius $0.1\text{m}$ under a centrifugal force of $4\times {10}^{-13}\text{N}$. If the mass of proton is $1.6\times {10}^{-27}\text{kg}$, the angular velocity of rotation is (in rad/s)

1. $2.5\times {10}^7$
2. $5\times {10}^7$
3. $5\times {10}^{14}$
4. $25\times {10}^{14}$

Q. A wheel is rotating at $900\text{rpm}$ about its axis. When power is cut off, it comes to rest in $60\text{s}$. The angular retardation is $\left(rad/s^2\right)$

1. $\frac{\pi }{2}$
2. $\frac{\pi }{4}$
3. $\frac{\pi }{6}$
4. $\frac{\pi }{8}$

Q. A particle is located at $(3,4)m$ and moving with velocity $\overrightarrow{v}=(4\hat{i}-3\hat{j})m/s$ . Find the magnitude of angular velocity about origin at this instant.

1. $2rad/s$
2. $1rad/s$
3. $0.5rad/s$
4. $2.5rad/s$

Q. A projectile is projected with a kinetic energy K. Its range is R. It will have the minimum kinetic energy, after covering a horizontal distance equal to

1. 0.25 R
2. 0.5 R
3. 0.75 R
4. R

Q. A particle is moving in a circle and its angular velocity is given as $\omega =\pi t$ where $\omega$ is in radians and $t$ is in seconds. Find the average angular velocity at the end of one half circle.

1. $\sqrt{100\pi }\text{rad/s}$
2. $\sqrt{90\pi }\text{rad/s}$
3. $\frac{\pi }{2}\text{rad/s}$
4. $\frac{\pi }{\sqrt{2}}\text{rad/s}$

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

Q. A small block is connected to one end of two identical massless strings of length $16\frac{2}{3}\text{cm}$ each with their other ends fixed to a vertical rod. If the ratio of tensions $\frac{T_1}{T_2}$ is $4:1$, then what will be the angular velocity of the block? [Take $g=9.8{\text{ms}}^{-2}$].

1. $7\text{rad/s}$
2. $8.5\text{rad/s}$
3. $11\text{rad/s}$
4. $14\text{rad/s}$

Q. Particle $P$ shown in figure is moving in a circle of radius $R=10cm$ with linear speed $v=2m/s$. Find the angular speed of particle about point $O$

1. $10\text{rad/s}$
2. $20\text{rad/s}$
3. $30\text{rad/s}$
4. $40\text{rad/s}$

Q. Two particles $A$ and $B$ are moving on two different concentric circles of radii $r_A$ and $r_B$ ($r_B>r_A$) with different velocities $V_A$ and $V_B$ respectively. Then angular velocity of $B$ as observed by $A$ is given by

1. $\frac{V_B-V_A}{r_B-r_A}$
2. $\frac{V_A}{r_A}$
3. $\frac{V_B}{r_B}$
4. $\frac{V_B+V_A}{r_B+r_A}$

Q. A particle starts moving from rest at $t=0$ with a tangential acceleration of constant magnitude of $\pi {\text{m/sec}}^2$ along a circle of radius $6\text{m}$. The values of average velocity and average speed during the first $2\sqrt{3}\text{seconds}$ of motion are

1. Average velocity $=2\sqrt{3}\text{m/s}$; Average speed $=\sqrt{3}\text{m/s}$
2. Average velocity $=2\sqrt{3}\text{m/s}$; Average speed $=\sqrt{3}\pi \text{m/s}$
3. Average velocity $=4\sqrt{3}\text{m/s}$; Average speed $=\sqrt{3}\pi \text{m/s}$
4. Average velocity $=\sqrt{3}\text{m/s}$; Average speed $=\sqrt{3}\pi \text{m/s}$

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