A large, cylindrical roll of tissue paper of initial radius R lies on a long, horizontal surface with the outside end of the paper nailed to the surface. The roll is given a slight shove (vi θ 0) and commences to unroll. Assume the roll has a uniform density and that mechanical energy is conserved in the process.
(a) Determine the speed of the center of mass of the roll when its radius has diminished to r.
(b) Calculate a numerical value for this speed at r = 1.00 mm, assuming R = 6.00 m.
(c) What If? What happens to the energy of the system when the paper is completely unrolled?