Angular Analogue of Linear Momentum

Q. Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:

1. $2:1$
2. $1:2$
3. $\sqrt{2}:1$
4. $1:\sqrt{2}$

Q.

If the net force acting on the system of particles is zero, then which of the following may vary

1. velocity of centre of mass

2. moment of inertia

3. position of centre of mass

4. Kinetic energy of the system

Q. A coin is of mass 4.8 kg and radius 1 m , is rolling on a horizontal surface without slipping, with an angular velocity of 600 rad/min.What is total kinetic energy is.

Q. if angular momentum of a rotating body about a fixed axis is increased by 10 percent then its kinetic energy is

Q.

uniform circular disc of mass 200 g and radius 4.0 cm is rotated about one of its diameter at an angular speed of 10 rad/s. Find the angular momentum about the axis of rotation

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Q. If the linear momentum is increased by 50%, then by what percentage will kinetic energy increase?

Q. In a graph between kinetic energy and momentum why is the line curved in case of P and not in case of P^{2 }?

Q. 88.A particle moves in a straight line with acceleration proportional to x²(where x is displacement). The gain of kinetic energy for any displacement is proportional to

Q. 35.a car of mass m is moving on a level circular track of radius R.Its coeffecient of static friction between road and tyres of car is represented by (meu)s , the maximum speed of car in circular motion is given by

Q. 13. A disc is undergoing pure rolling motion with speed v the radius of the disk being r and mass m then the angular momentum of the disc about the bottom most point will be having magnitude equal to

Q. A Wheel of mass 8 kg and radius 40cm is rolling on a horizontal road with angular velocity 15 rad/s. if M.I. of wheel about its axis is 0.64 kgm^2, then rolling kinetic energyof wheel is?

Q. A solid body rotates about a fixed axis such that itsangular velocity depends on θ as ω=kθ-1 where k is a positive constants. At t= 0, θ = 0, then timedependence ofθ is given as(1) kt(2) 0 2kt4) 0 2kt

Q. What is the derivation of relation between kinetic energy and linear momentum?

Q. A car goes on horizontal circular road of radius 4 m. The speed of car is increasing at a constant rate of3 m/s2. The friction coefficient between road and tyre is 0.5. Find the speed at which the car will skid.

Q. Two spheres each of mass M each moving with velocity U moving in different directions at 30 degree south of East and 30 degree north of East respectively colloid at point O and stick to each other the velocity of the combination later becomes what ​

Q. 25.Show that or derive an expression for the kinetic energy of a rotating body about a given axis is equal to 1/2 Lw, whre, L is angular momentum and w is angular velocity. i.e. K.E.=1/2 Lw

Q. Is angular momentum conserved in non uniform circular motion?

Q. A solid body rotates about a statinary axis so that its angular velocity depends on the rotalional angle φ as w=wo-ko, where wo & k are positive constants. At the moment t=0, the angle φ=0. Find the time dependence of rotation angle.

Q. A solid cylinder of mass 2 kg and radius 0.2 mis rotating about its own axis without friction with angular velocity 3 rad/s. A particle of mass 0.5 kg moving with a velocity 5 m/s strikes the cylinder and sticks to it as shown in figure below. The angular momentum of the cylinder before collision will be

1. 0.12 J-s
2. 12 J-s
3. 1.2 J-s
4. 1.1.2 J-s

Q. 21. Consider the L shaped bar shown in figure. At the instant shown, the bar is rotating at 4 rad/s and is slowingdown at the rate of 2 rad/s?у-axisВori hugiguoto noitani2 mWlMotorX-аxisА2m -Find the acceleration of point A.of point B with respect to point A.b. Find the relative acceleration awheel of radius 0.5 m is spinning with a constant angular velocity of 2 rad/s. What is the centrip

Q.

Two small balls A and B, each of mass m, are attached rigidly to the ends of a light rod of length d. The structure rotates about the perpendicular bisector of the rod at an angular speed $\omega$. Calculate the angular momentum of the system about the axis of rotation.

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Q. Angular velocity of the particle becomes four times of its initial angular velocity in two seconds if initial angular velocity of a particle is 4RAD per second then average angular acceleration of particle is

Q.

uniform circular disc of mass 200 g and radius 4.0 cm is rotated about one of its diameter at an angular speed of 10 rad/s. Find the angular momentum about the axis of rotation

1. $4\times {10}^{-4}J-s$

2. $8\times {10}^{-4}J-s$

3. $4\times {10}^{-8}J-s$

4. $8\times {10}^{-8}J-s$

Q. if the angular momentum of a rotating body is increased by 200%, then its kinetic energy of rotation will increased by 1) 400% 2) 800% 3) 200% 4) 100

Q. A ball of mass 'm' is left at the top of an inclined plane of heght 'h' . At the foot of the plane, if the ball has to complete a vertical circle of radius R what is the least value of h ?

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Q.

Match the block diagrams of block of mass (m) with their corresponding free body diagram (every surface is frictionless)

(bodies are at rest with respect to ground)

1. P = (ii); Q - (ii); R - (iii)

2. P = (iv); Q - (i); R - (iii)

3. P = (iii); Q - (iii); R - (iii)

4. P = (iii); Q - (ii); R - (iii)

Q. A whell of mass 2kg having practically all the mass concentrated along the circumference of a circle of radius 20 cm, os rotating on ita axis with an angular velocity 100 rad/sec. The rotational kinetic energy of the wheel is

Q. A disc of mass M kg and radius R metre is rotating at an angular speed of w rad/s when the motor is switched off. Neglecting the friction at the axle, the force that must be applied tangentially to the wheel to bring it to rest in time t is

Q.

A uniform rod of mass 'm' and Length 'L' is rotated about its perpendicular bisector at an angular speed $\omega$. Calculate its angular momentum about its Axis of rotation?

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Q. if a cyclist moving with a speed of 4.9m/s on a level road can take a sharp circular turn of radius 4 m , then coefficient of friction btw cyclist tyres and road is