A particle of mass m is attached to the end of a light string of length l. The other end of the string is passed through a small hole and is slowly pulled through it. Gravity is negligible. The particle is originally spinning the round the hole with angular velocity w. Find the angular velocity when the string length has been reduced to 1/2 l. Find also the tension in the string when its length is r, and verify that the increase in kinetic energy is equal to the work done by the force pulling the string through the hole.
Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.
Let the length of the string at any time t be r. Let the tension be T(r). Let ...
The ball in this problem is constrained to move on the surface of a table. Typically, this type of problem requires one to use Lagrangian mechanics. However, here I have used the conservation of angular momentum. I have provided all the necessary steps in arriving at the solution.