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The distances between the different particles in a rigid body stay constant. The geometrical centre of mass is always at the geometrical centre of regular shaped bodies with uniform mass distribution. In a rigid item, net torque causes it to turn.
If the total external force acting on a rigid body is zero, it is said to be in translational equilibrium. If the entire external torque on it is zero, it is in rotational equilibrium. An extended body’s centre of gravity is the point where the entire gravitational torque on the body is zero. The component of angular momentum along the axis of rotation is constant if the external torque acting on the body is zero.
For each translational quantity, there exist rotational equivalents. The translational and rotational motions are combined in a rolling motion. The transient rotation about the point of contact can also be referred to as rolling. The total kinetic energy of pure rolling is the sum of the kinetic energies of translational and rotational motions.
The translational motion in sliding is greater than the rotating motion. The rotational motion is greater than the translational motion when slipping.
1. The mass centre of a system of particles is independent of,
(a) position of particles
(b) relative distance between particles
(c) masses of particles
(d) force acting on particle
Answer: (d) force acting on particle
2. What does a couple produce?
(a) pure rotation
(b) pure translation
(c) rotation and translation
(d) no motion
Answer: (a) pure rotation
3. A particle moves down a line parallel to the positive X-axis at a constant speed. With respect to the origin, the magnitude of its angular momentum is,
(a) zero
(b) increasing with x
(c) decreasing with x
(d) remaining constant
Answer: (d) remaining constant
4. A rope is looped around a hollow cylinder with a radius of 40 cm and a mass of 3 kg. If the rope is pulled with a force of 30 N, what is the angular acceleration of the cylinder?
(a) 0.25 rad s-2
(b) 25 rad s-2
(c) 5 m s-2
(d) 25 m s-2
Answer: (b) 25 rad s-2
5. Water is half filled into a closed cylindrical container. As the container rotates in a horizontal plane about a perpendicular bisector, what will be the effect on the moment of inertia?
(a) increases
(b) decreases
(c) remains constant
(d) depends on direction of rotation.
Answer: (a) increases
6. With an angular momentum of L, a rigid body rotates. What will be the angular momentum becomes, if the kinetic energy is halved?
(a) L
(b) L/2
(c) 2L
(d) L/ 2
Answer: (d) L/ 2
7. A particle moves in a circular motion that is consistent. The particle’s angular momentum will be conserved about,
(a) the centre point of the circle.
(b) the point on the circumference of the circle.
(c) any point inside the circle.
(d) any point outside the circle.
Answer: (a) the centre point of the circle.
8. The angular momentum of a mass revolving in a plane around a fixed point is directed along,
(a) a line perpendicular to the rotation plane
(b) the line that forms a 45° angle with the rotation plane
(c) the radius
(d) tangent to the path
Answer: (a) a line perpendicular to the rotation plane
9. Two discs with the same moment of inertia rotate at angular velocities 1 and 2 around their regular axis, which passes through the centre and is perpendicular to the disc plane. They’re brought in face to face, with the axis of rotation aligned between them. During this process, the equation for energy loss is,
(a) 1/4 I (ω1– ω2)2
(b) I (ω1– ω2)2
(c) 1/8 I (ω1– ω2)2
(d) 1/2 I (ω1– ω2)2
Answer: (a) 1/4 I (ω1– ω2)2
10. The acceleration of a solid sphere (mass m, radius R) rolling down an incline of angle without slipping versus slipping down the slope without rolling is,
(a) 5:7
(b)2:3
(c) 2:5
(d) 7:5
Answer: (a) 5:7
11. From a disc of radius R a mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through it
(a) 15MR2/32
(b) 13MR2/32
(c) 11MR2/32
(d) 9MR2/32
Answer: (b) 13MR2/32
12. The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is,
(a) √4gh/3
(b) √10gh/7
(c) √2gh
(d) √1gh/2
Answer: (a) √4gh/3
13. The centre of a wheel rolling on a horizontal surface has a velocity of vo. A point on the rim that is level with the centre will move at a rate of,
(a) zero
(b) vo
(c) √2vo
(d) 2vo
Answer: (c) √2vo
14. A round object of mass M and radius R rolls down without slipping along an inclined plane. The frictional force,
(a) dissipates kinetic energy as heat.
(b) Rotational motion is reduced.
(c) reduces rotational and transnational movement
(d) Transnational energy is converted into rotational energy.
Answer: (d) Transnational energy is converted into rotational energy.
15. The moment of inertia of an item does not depend on which of the following factors?
(a) Axis of rotation
(b) Angular velocity
(c) Distribution of mass
(d) Mass of an object
Answer: (b) Angular velocity
16. What is the frictional force exerted by a round object of mass M and radius R rolling down an inclined plane without slipping?
(a) The spinning action has slowed down.
(b) The rotational and translational motions are reduced.
(c) There is a translational motion to rotational motion conversion.
(d) Heat is created when kinetic energy is transformed.
Answer: (c) There is a translational motion to rotational motion conversion.
17. Consider two objects, a disc and a sphere, with the same radius but different masses, rolling down two inclined planes of equal height and length. Which of the two things is the first to reach the plane’s bottom?
(a) It is determined by the object’s mass.
(b) Disk
(c) Sphere
(d) Both reach at the same time
Answer: (c) Sphere
18. The motion of planets in the solar system is an example of conservation of
(a) Energy
(b) Linear momentum
(c) Angular momentum
(d) Mass
Answer: (c) Angular momentum
