Rotational Mechanics Physics - Rotational Mechanics

A sphere is rolled on a rough horizontal surface. It gradually slows down and stops. The force of friction tries to:

1. Decrease the linear velocity.
2. Increase the angular velocity.
3. Increase the linear momentum.
4. Decrease the angular velocity.

A wheel of radius 20cm is pushed to move it on a rough horizontal surface. It is found to move through a distance of 60cm on they road during the time it completes one revolution about the centre. Assume that the linear and the angular accelerations are uniform. The frictional force acting on the wheel by the surface is:

1. Along the velocity of the wheel.
2. Opposite to the velocity of the wheel.
3. Perpendicular to the velocity of the wheel.
4. Zero.

A body is rotating uniformly about a vertical axis fixed in an inertial frame. The resultant force on a particle of the body not on the axis is:

1. Vertical.
2. Horizontal and skew with the axis.
3. Horizontal and intersecting the axis.
4. None of these.

A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance 1 from the cylinder holds one end of the string and pulls the cylinder towards him. There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is:

1. l
2. 2l
3. 3l
4. 4l

A hollow sphere, a solid sphere, a disc and a ring all having same mass and radius are rolled down on an inclined plane. If no slipping takes place, which one will take the smallest time to cover a given length?

A simple pendulum is a point mass suspended by a light thread from a fixed point. The particle is displaced towards one side and then released. It makes small oscillations. Is the motion of such a simple pendulum a pure rotation? If yes, where is the axis of rotation?

Can an object be in pure translation as well as in pure rotation?

If the ice at the poles melts and flows towards the equator, how will it affect the duration of day-night?

When a body is weighed on an ordinary balance we demand that the arm should be horizontal if the weights on the two pans are equal. Suppose equal weights are put on the two pans, the arm is kept at an angle with the horizontal and released. Is the torque of the two weights about the middle point (point of support) zero? Is the total torque zero? If so, why does the arm rotate and finally become horizontal?

A cylinder rolls on a horizontal plane surface. If the speed of the centre is 25m/s, what is the speed of the highest point?

The torque of the weight of any body about any vertical axis is zero. Is it always correct?

Suppose the platform of the previous problem is brought to rest with the ball in the hand of the kid standing on the rim. The kid throws the ball horizontally to his friend in a direction tangential to the rim with a speed v as seen by his friend. Find the angular velocity with which the platform will start rotating.

A heavy particle of mass m falls freely near the earth's surface. What is the torque acting on this particle about a point 50cm east to the line of motion? Does this torque produce any angular acceleration in the particle?

Find the moment of inertia of a pair of spheres, each having a mass m and radius r, kept in contact about the tangent passing through the point of contact.

A wheel of mass 10kg and radius 20cm is rotating at an angular speed of 100rev/min when the motor is turned off. Neglecting the friction at the axle, calculate the force that must be applied tangentially to the wheel to bring it to rest in 10 revolutions.

Find the angular velocity of a body rotating with an acceleration of 2 rev/s² as it completes the 5^th revolution after the start.

A wheel rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.

A light rod of length 1m is pivoted at its centre and two masses of 5kg and 2kg are hung from the ends as shown in figure. Find the initial angular acceleration of the rod assuming that it was horizontal in the beginning.

A disc of radius 10cm is rotating about its axis at an angular speed of 20rad/s. Find the linear speed of:

1. A point on the rim.
2. The middle point of a radius.

The moon rotates about the earth in such a way that only one hemisphere of the moon faces the earth. Can we ever see the ''other face'' of the moon from the earth? Can a person on the moon ever see all the faces of the earth?

A kid of mass M stands at the edge of a platform of radius R which can be freely rotated about its axis. The moment of inertia of the platform is I. The system is at rest when a friend throws a ball of mass m and the kid catches it. If the velocity of the ball is v horizontally along the tangent to the edge of the platform when it was caught by the kid, find the angular speed of the platform after the event.

When a fat person tries to touch his toes, keeping the legs straight, he generally falls. Explain with reference to figure.

A ladder is resting with one end on a vertical wall and the other end on a horizontal floor. Is it more likely to slip when a man stands near the bottom or near the top?

When tall buildings are constructed on earth, the duration of day-night slightly increases. Is it true?

Two small balls A and B, each of mass m, are joined rigidly to the ends of a light rod of lengh L (figure). The system translates on a frictionless horizontal surface with a velocity vo in a direction perpendicular to the rod. A particle P of mass m kept at rest on the surface sticks to the ball A as the ball collides with it. Find:

1. The linear speeds of the balls A and B after the collision.
2. The velocity of the centre of mass C of the system A + B + P.
3. The angular speed of the system about C after the collision.

[Hint: The light rod will exert a force on the ball B only along its length.]

Suppose the friction coefficient between the ground and the ladder of the previous problem is 0.540. Find the maximum weight of a mechanic who could go up and do the work from the same position of the ladder.

A uniform metre stick of mass 200g is suspended from the ceiling through two vertical strings of equal lengths fixed at the ends. A small object of mass 20g is placed on the stick at a distance of 70cm from the left end. Find the tensions in the two strings.

Suppose the smaller pulley of the previous problem has its radius 5.0cm and moment of inertia 0.10kg-m². Find the tension in the part of the string joining the pulleys.

The door of an almirah is 6ft high, 1.5ft wide and weighs 8kg. The door is supported by two hinges situated at a distance of 1ft from the ends. If the magnitudes of the forces exerted by the hinges on the door are equal, find this magnitude.