Direction of Angular Velocity

Q.

The boy running along a circular track of radius 7m and he completes one orbit in 10 seconds. find average speed and velocity.

Q. If a particle is rotating in circular path, the direction of the angular velocity is along

1. towards centre
2. the tangent of the circular path
3. away from centre
4. the axis of rotation

Q. A particle is moving along a circular path with uniform speed. Through what angle does its angular velocity changes when it completes half of the circular path?

1. $0^{\circ }$
2. ${45}^{\circ }$
3. ${180}^{\circ }$
4. ${360}^{\circ }$

Q. A particle of mass 2kg is moving in circular path with constant speed 20 m/s. Find the magnitude of change in velocity when particle moved such that line joining the particle to center sweeps the angle 90^° .

Q.

The second’s hand of a clock is $10cm$ long. It goes round once every $60seconds$.
(a) What is the average speed of the tip of the second hand?
(b) What is the distance travelled by the tip in $10seconds$?
(c) What is its average velocity during the time it makes one revolution? (Take $\mathrm{\pi }=3.14$)

Q. A particle is moving along a circular path with uniform speed. Through what angle does its angular velocity change when it completes half of the circular path?

1. ${45}^{\circ }$
2. ${180}^{\circ }$
3. ${360}^{\circ }$
4. $0^{\circ }$

Q. Find the total energy of the inclined rod of mass $m$, rotating with an angular velocity $\omega$ about a vertical axis $Y{Y}^{\prime }$ as shown in figure.

1. $\frac{m{\omega }^2{l}^2}{12}$
2. $\frac{m{\omega }^2{l}^2}{24}$
3. $\frac{m{\omega }^2{l}^2}{36}$
4. $\frac{m{\omega }^2{l}^2}{48}$

Q. A projectile is thrown at a speed of 20 m/s at an angle of ${53}^{\circ }$ with the horizontal. When it is at the highest point, its center of curvature is at $(g=10m/s^2)$

1. Ground
2. 1.2 m below ground
3. 1.6 m below ground
4. 2 m above ground

Q. A heavy particle hangs from a point O, by a string of length a. It is projected horizontally with a velocity $v=\sqrt{(2+\sqrt{3})ag}$.
The angle with the upward vertical, string makes where string becomes slack is

1. $\theta =si{n}^{-1}\left(\frac{-1}{\sqrt{3}}\right)$
2. $\theta =co{s}^{-1}\left(\frac{1}{\sqrt{3}}\right)$
3. $\theta =co{s}^{-1}\left(\frac{1}{\sqrt{2}}\right)$
4. $\theta =si{n}^{-1}\left(\frac{1}{\sqrt{2}}\right)$

Q. Define angular velocity and angular acceleration. Obtain relation between linear velocity and angular velocity.

Q. If a particle is rotating in circular path, the direction of the angular velocity is along

1. the tangent of the circular path
2. towards centre
3. away from centre
4. the axis of rotation

Q. If a particle is moving clockwise in a circle in $x-y$ plane with centre at origin, the direction of angular velocity of the particle is

1. $\hat{k}$
2. $-\hat{j}$
3. $\hat{i}$
4. $-\hat{k}$

Q.

A particle moves with constant angular velocity in a circle. During the motion its

1. Energy is conserved

2. Momentum is conserved

3. Energy and momentum both are conserved

4. None of the above is conserved

Q.

How are linear velocity and angular velocity related?

Q. State Right hand rule with a labelled diagram.

Q. nta particle moving in a circular pah. the acceleration and momentum of the particle at a certain moment are a=4i+3j and P =8i-6j.the otion of the particle isn ntuniform circlarn ntaccelerated circularn ntdeacc circularn ntnonen

Q. A particle is thrown from point B as shown in figure. At this moment of time, the angular speed of particle with respect to an axis passing through point A and perpendicular to plane of figure is

1. $\frac{\left(v_b\sin 2{\theta }_b\right)}{r}$
2. $\frac{(-v_b)}{r}$
3. $\frac{\left(v_b\sin {\theta }_b\right)}{r}$
4. $\frac{\left(v_b\right)}{r}$

Q. A small object placed on a rotating horizontal turn table just slips when it is placed at a distance $4\text{cm}$ from the axis of rotation. If the angular velocity of the turn-table is doubled, the object slips when its distance from the axis of rotation is (in $\text{cm}$)

Q.

A person standing on the top of a cliff 171 ft high has to throw a packet to his friend standing on the ground 228 ft horizontally away. If he throws the packet directly aiming at the friend at the friend wuth a speed of 15.0 ft/s, how short will the packet fall ?

Q. A particle is moving along a circular path. The angular velocity, linear velocity, angular acceleration, and centripetal acceleration of the particle at any instant respectively are $\overrightarrow{\omega },\overrightarrow{v},\overrightarrow{\alpha }$, and $\overrightarrow{a_c}$. Which of the following relations is not correct?

1. $\overrightarrow{\omega }\perp \overrightarrow{v}$
2. $\overrightarrow{\omega }\perp \overrightarrow{\alpha }$
3. $\overrightarrow{\omega }\perp \overrightarrow{a_c}$
4. $\overrightarrow{v}\perp \overrightarrow{a_c}$

Q.

If the angular velocity of a disc depends on an angle rotated as ω=(θ²+θ), then its angular acceleration at θ=1 rad is

1. $3rad/s^2$

2. $6rad/s^2$

3. $2rad/s^2$

4. $9rad/s^2$

Q. A circular disc of radius R rolls without slipping along the horizontal surface with constant velocity $v_0$. We consider a point P on the surface the disc. Then, the acceleration of the point P is :

1. Constant in Magnitude
2. Constant in magnitude as well as direction
3. Constant in direction
4. None of the above

Q. A fan starts rotating with an angular acceleration $2{\text{rad/s}}^2$. After it accelerates for $5\text{s}$, for next $5\text{s}$ it rotated with constant velocity & then deaccelerates for next $10\text{s}$ & stops. Find the total number of rotations.

1. $\frac{255}{\pi }$
2. $\frac{60}{\pi }$
3. $\frac{125}{2\pi }$
4. $\frac{120}{\pi }$

Q. For a particle moving along a circular path with a constant speed, the acceleration is constant in

1. Both magnitude and direction
2. Neither magnitude nor direction
3. Magnitude
4. Direction

Q. Two particles A and B perform SHM along the straight line with the same amplitude ${}^{\prime }{a}^{\prime }$, same frequency ${}^{\prime }{f}^{\prime }$ and same equilibrium position ${}^{\prime }{O}^{\prime }$. The greatest distance between them is found to be $\frac{3a}{2}$. At some instant of time, they have the same displacement from mean position. What is the displacement?

Q. A projectile is thrown at a speed of 20 m/s at an angle of ${53}^{\circ }$ with the horizontal. When it is at the highest point, its center of curvature is at $(g=10m/s^2)$

1. Ground
2. 1.6 m below ground
3. 2 m above ground
4. 1.2 m below ground

Q. If a particle is rotating in circular path, the direction of the angular velocity is along

1. the tangent of the circular path
2. towards centre
3. away from centre
4. the axis of rotation

Q. The figure below shows a pattern of two fishes. Write the mapping rule for the rotation of Image A to Image B.

1. Image B has to be rotated by 90 degrees anticlockwise to map with image A
2. Image B should first have a mirror reflection and then be rotated to map with image A
3. The width of image B should be reduced by 1 unit (1 square in the graph shown) and then rotated by 90 degrees to map with image A
4. The width of image B should be increased by 1 unit (1 square in the graph shown) and then rotated by 90 degrees to map with image A

Q. A projectile is thrown at a speed of 20 m/s at an angle of ${53}^{\circ }$ with the horizontal. When it is at the highest point, its center of curvature is at $(g=10m/s^2)$

1. Ground
2. 1.6 m below ground
3. 2 m above ground
4. 1.2 m below ground

Q. Trajectory of a projectile near the surface of Earth is $y=4x-12x^2$. If $y$ is vertical axis and $x$ is horizontal then angle of projection is

1. $ta{n}^{-1}\left(1\right)$
2. $ta{n}^{-1}\left(4\right)$
3. $ta{n}^{-1}\left(\sqrt{3}\right)$
4. $ta{n}^{-1}\left(\sqrt{2}\right)$