Questions 1-2

1. A thin-walled hollow cylinder (mass = mn, radius = Th) and a solid cylinder (mass = ms, radius = [s) start from rest at the top of an incline. Both cylinders start rolling down the incline without slipping at a vertical height of ho. Ignoring the air resistance, determine in a symbolic expression the translational speed of each cylinder upon arriving at the bottom of the incline (note that In = math" Is = 12 mrs2). 2. Two spheres are each rotating at an angular speed of 38.0 rad/s about axes which pass through their centers. Each has a radius of 0.350 m and a mass of 1.98 kg. However, one is solid and the other is a thin-walled spherical shell. If a net external torque due to say friction of magnitude 0.678 n.m applies to each sphere and slows their motion down, how long does it take for each sphere to come to a rest? (note that spherical shell = 2/3 MR, Isolid sphere = 2/5 MR2)