Angular Velocity

Q.

A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. 4.21. If the round trip takes 10 min, what is the (a) net displacement, (b) average velocity, and (c) average speed of the cyclist ?

Q.

The earth $(mass=6\times {10}^{24}kg)$ revolves around the sun with angular velocity $2\times {10}^{-7}rad/s$ in a circular orbit of radius $1.5\times {10}^{8}km$. The force exerted by the sun on the earth in newtons is

1. 

2. Zero

3. 

4. 

Q. rain is falling with speed 4m/s in in direction making angle 30 degrees with vertical towards north. What should be magnitude and direction of velocity of cyclist to hold his umbrella exactly vertical so that rain does not wet him?

Q. if a particle is moving on a circular path with constant speed, then the angle between the direction of acceleration and its position vector w.r.t. centre of circle will be

Q. the angular momentum of system of particle is conserved when no external force acts upon the system. is this statement true

Q. A particle is moving with uniform acceleration along a straight line ABC. Its velocity atA and Bare 6 m/s and 9 m/s respectively.If AB BC 5:16 then its velocity at C is

Q. A circular disc rotates freely about a vertical axis through its centre with angular velocity ω1 . A ring having the same mass and radius of the disc is placed on the disc and the system now rotates with an angular velocity ω2 about the same vertical axis. Then ω2/ω1 is

Q.

A body tied with string revolves uniformly in a circle. How does the angular momentum of the body change from its initial value if the string is cut suddenly?

1. It becomes zero

2. It increases

3. It decreases

4. It remains same

Q.

If a particle moves in a circle describing equal angles in equal intervals of time, its velocity vector

1. Remains constant

2. Changes in magnitude

3. Changes in direction

4. Changes both in magnitude and direction

Q. Rain drop appears to fall in vertical direction to a person who is walking at a velocity of 8 m/s in a given direction . When the person doubles his velocity in the same direction , the rain drop appears to make an angle 45^†extdegree with the vertical .Find the speed of the rain drop

Q. A small ball is given a velocity\surd2gl on the smooth horizontal floor which leads to a smooth vertical circular path. the ball will

Q. a particle is performing circular motion in a circle of radius R with variable speed, v=Kt (k>0).time when angle between acceleration vector and its velocity vector becomes pi/4, is 4 root (R/nk).the value of n is

Q. 68. A solid sphere spinning about a horizontal axis with an angular velocity w is placed on a horizontal surface. Subsequently it rolls without slipping with an angular velocity of (A) 2 w/5 (B) 7 w/5 (C) 2 w/7 (D) w

Q. How velocity is always ahead of displacement by phase angle π/2 radian??

Q. Two points $A$ and $B$ on a disc have velocities $v_1$ and $v_2$ at some moment. Their directions make angles ${60}^o$ and ${30}^o$ respectively with the line of separation as shown in the figure. The angular velocity of the disc is:

1. $\frac{\sqrt{3}{v}_1}{d}$
2. $\frac{v_2}{\sqrt{3}d}$
3. $\frac{v_2-v_1}{d}$
4. $\frac{v_2}{d}$

Q. A cannon ball is fired at a speed of $50m{s}^{-1}$, where the angle of projection is ${30}^{\circ }$. Find the maximum height and also the time of flight of the cannon ball. (Take acceleration due to gravity, $g=10m{s}^{-2}$).

1. T = 5 s, H = 31.25 m

2. T = 11 s, H = 31.25 m

3. T = 5 s, H = 45.6 m

4. T = 10 s, H = 45.1 m

Q.

Two particles of mass m each are attached to a light rod of length d, one at its centre and the other at a free end. The rod is fixed at the other end and is rotated in a plane at an angular speed $\omega$. Calculate the angular momentum of the particle at the end with respect to the particle at the centre (i.e. angular momentum of B with respect to A).

1. 

2. 

3. 

4. 

Q. A flywheel rotates at a costant speed of $3000$ rpm. How much time will it take to describe the angle of 100$\pi$ rad?

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

Q. Two steel balls of equal diameter are connected by a rigid bar of negligible weight as shown and are dropped in the horizontal position from height $h$ above the heavy steel and brass base plates. If the coefficient of restitution between the ball and the steel base is $0.6$ and that between the other ball and the brass base is $0.4$, the angular velocity of the bar immediately after rebound is (Assume the two impacts are simultaneous and take $g=10{\text{m/s}}^2$).

1. $\frac{2}{5}\text{rad/s}$
2. $\frac{1}{5}\text{rad/s}$
3. $\frac{3}{5}\text{rad/s}$
4. $\frac{1}{4}\text{rad/s}$

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

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

Q. A particle covers equal distances around a circular path in equal intervals of time. It has uniform non-zero rate of change of

1. linear displacement
2. angular displacement
3. linear velocity
4. angular velocity

Q. A diver makes $4\text{revolutions}$ on the way from a $4.9\text{m}$ platform above the water surface. Assuming zero initial vertical velocity, calculate the average angular velocity of the diver. [Take $g=9.8m/s^2$]

1. $8\pi \text{rad/s}$
2. $4\pi \text{rad/s}$
3. $2\pi \text{rad/s}$
4. $\pi \text{rad/s}$

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. 10.47 deg/s

4. 60 deg/s

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. 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

Q. What is the angular velocity (in rad/s) of a fly wheel making 300 r.p.m?

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

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. Two cars having masses $m_{1}and{m}_2$ move in circles of radii $r_{1}and{r}_2$ respectively. If they complete the circle in equal time, the ratio of their angular speeds $\frac{{\omega }_1}{{\omega }_2}$ is _______

1. 

2. 

3. 

4. 1

Q. The angular velocity of a rigid body about any point of that body is same

1. only in magnitude
2. only in direction
3. both in magnitude and direction necessarily
4. both in magnitude and direction about some points but not about all points.

Q. Two bodies $A$ and $B$ rotate about an axis, such that angle ${\theta }_A$ (in radians) covered by the first body is proportional to square of time, and ${\theta }_B$ (in radians) covered by the second body varies linearly. At $t=0,{\theta }_A={\theta }_B=0$. If $A$ completes its first revolution in $\sqrt{\pi }\text{sec}$ and $B$ needs $4\pi \text{sec}$ to complete half a revolution, then angular velocity ${\omega }_A$ and ${\omega }_B$ at $t=5\text{sec}$ are in the ratio

1. 4 : 1
2. 20 : 1
3. 80 : 1
4. 20 : 4