FYKOS Year 35 Series 3 Problem 2 — playing with keys · FYKOS 35 #35.3.2
Physics · mechanics
Problem
Vašek likes to plays with keys by swinging them around on a keychain and then letting them wrap around his hand. We will simplify this situation by a model, in which we have a point mass m in weightlessness attached to an end of massless keychain of length l0. The other end of the keychain is attached to a solid cylinder of radius r. The keychain is taut so that it is perpendicular to the surface of the cylinder at the attachment point, and the point mass is then brought to velocity \vectv0 in the direction perpendicular both to the axis of the cylinder and to the direction of the keychain. The keychain then starts to wrap around the cylinder. What is the dependence of the velocity of the point mass on the length of the free (not wrapped around) keychain l?