Rotational Mechanics Physics - Rotational Mechanics

A particle moves on a straight line with a uniform velocity. Its angular momentum:

1. Is always zero.
2. Is zero about a point on the straight line.
3. Is not zero about a point away from the straight line.
4. About any given point remains constant.

A hollow sphere and a solid sphere having same mass and same radii are rolled down a rough inclined plane:

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.

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?

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.

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

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.

If several forces act on a particle, the total torque on the particle may be obtained by first finding the resultant force and then taking torque of this resultant. Prove this. Is this result valid for the forces acting on different particles of a body in such a way that their lines of action intersect at a common point?

A uniform rod of mass 300g and length 50cm rotates at a uniform angular speed of 2rad/s about an axis perpendicular to the rod through an end. Calculate:

1. The angular momentum of the rod about the axis of rotation.
2. The speed of the centre of the rod.
3. Its kinetic energy.

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

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 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?