Rotational Mechanics Physics - Rotational Mechanics

The angular velocity of the engine (and hence of the wheel) of a scooter is proportional to the petrol input per second. The scooter is moving on a frictionless road with uniform velocity. If the petrol input is increased by 10%, the linear velocity of the scooter is increased by:

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

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 rectangular brick is kept on a table with a part of its length projecting out. It remains at rest if the length projected is slightly less than half the total length but it falls down if the length projected is slightly more than half the total length. Give reason.

If the angular momentum of a body is found to be zero about a point, is it necessary that it will also be zero about a different point?

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.

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

A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100rev/sec in 4 seconds. Find the angular acceleration. Find the angle rotated during these four seconds.

A string is wrapped over the edge of a uniform disc and the free end is fixed with the ceiling. The disc moves down, unwinding the string. Find the downward acceleration of the disc.

Three particles, each of mass 200g, are kept at the corners of an equilateral triangle of side 10cm. Find the moment of inertia of the system about an axis:

1. Joining two of the particles.
2. Passing through one of the particles and perpendicular to the plane of the particles.

A thin spherical shell lying on a rough horizontal surface is hit by a cue in such a way that the line of action passes through the centre of the shell. As a result, the shell starts moving with a linear speed v without any initial angular velocity. Find the linear speed of the shell after it starts pure rolling on the surface.

A cylinder rotating at an angular speed of 50rev/s is brought in contact with an identical stationary cylinder. Because of the kinetic friction, torques act on the two cylinders, accelerating the stationary one and decelerating the moving one. If the common magnitude of the acceleration and deceleration be one revolution per second square, how long will it take before the two cylinders have equal angular speed?

A metre stick weighing 240g is pivoted at its upper end in such a way that it can freely rotate in a vertical plane through this end (figure). A particle of mass 100g is attached to the upper end of the stick through a light string of length 1m. Initially, the rod is kept vertical and the string horizontal when the system is released from rest. The particle collides with the lower end of the stick and sticks there. Find the maximum angle through which the stick will rise.

A uniform rod pivoted at its upper end hangs vertically. It is displaced through an angle of 60° and then released. Find the magnitude of the force acting on a particle of mass dm at the tip of the rod when the rod makes an angle of 37° with the vertical.

A ball is whirled in a circle by attaching it to a fixed point with a string. Is there an angular rotation of the ball about its centre? If yes, is this angular velocity equal to the angular velocity of the ball about the fixed point?

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.

Particles of masses 1g, 2g, 3g, ........, 100g are kept at the marks 1cm, 2cm, 3cm, ........, 100cm respectively on a metre scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.

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?

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

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?

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.