A disc of mass M, which may be considered to be a point mass, is placed on a frictionless horizontal table. A massless string is fastened to the disc and is passed through a small hole at the centre of the table. The lower end of the string is tied to the end of a flexible rope of mass m per unit length which lies on the floor just under the hole in the table. Initially the lower end of the massless string is held firmly just at floor level and the disc is made to move in a circle, radius r0 about the hole, with a velocity of constant magnitude v0.
At a subsequent time, the end of the massless string is released from the floor, allowing the radius r of the circular motion of the disc to vary and the rope to be lifted off the floor. You may assume that the contact point between the rope and the floor remains vertically below the hole in the table and may neglect the effects of any horizontal motion of the rope along the floor.
The subsequent velocity of the disc has a radial component vr and an azimuthal component v∅. Show that the azimuthal component of the velocity is given by v∅ = v0r0/r.
The Attempt at a Solution
Need a quantity that is conserved under the change of situation. Is it angular momentum?