Impulse and Momentum

Conservation of angular momentum:

If the resultant moment about a fixed point O of all forces acting on a particle is zero during an interval of time, then its angular mometum remains constant.

Also the total angular momentum for the system of the two particles remains constant during the interval.

An Example:

A particle of mass m tied at the end of an extensible string is rotated at rad/sec along a circle of r radius over a smooth horizontal table top. The string is pulled down through a slot at the center of the table top at a speed V. Calculate the speed of the particle when it reaches r/2 from the center.

Solution:

The particle acted upon by three forces, the force of gravity, the normal reaction of the table (which is equal to the force of gravity) and the tension of the string. The moment of the resultant force about the center is zero, i.e.,