A mass m is attached to a cord passing through a small hole in a frictionless, horizontal surface. The mass is initially orbiting with speed vi in a circle of radius ri. The cord is then slowly pulled from below, and the radius of the circle decreases to r. (Use r_i for ri, v_i for vi, m, and r as appropriate in your equations below.)

Question

(a) What is the speed of the mass when the radius is r?
(b) Find the tension in the cord as a function of r
(c) How much work W is done in moving m from ri to r? (Note: The tension depends on r.)

Do you just use conservation of energy for this? Is it just rotational energy?

Answer 1

use conservation of angular momentum, it is easier. Angularmomentum=Vi/ri * mi
But you can use energy if you wish.