A point-like object of mass m is constrained to a straight fictionless massless rail that is free to spin about the % axis passing through the origin. The point mass is kept at a radius r by a taut string (see figure). The motor on the object can change the length of the string very slowly: the radial velocity and rate of change of angular velocity can be neglected in the calculations (when larger terms are present). Initially, the rail is spinning at w = wpZ and the object is at a fixed at a distance of ry from the origin. a) Find the angular momentum of the system about the origin. b) Find the kinetic energy of the system after the motor decreased the string length to r