Don't hula hoop on a hill

One hoop and one solid disk roll without slipping down a hill angled 30 degrees with respect to the horizontal. Each starts from rest such that their center of mass is 5.5 m above ground level. The hoop has mass 1 kg, radius 0.5 m, and is empty inside - all the mass is concentrated in a thin ring along the outside of the hoop. When the hoop reaches the bottom of the hill the speed of the center of mass of the hoop is \(v_h\). The disk also has mass 1 kg and radius 0.5 m, but the mass is distributed evenly throughout the disk. When the disk reaches the bottom of the hill the speed of the center of mass of the disk is \(v_d\). What is \(v_d/v_h\)?

Details and assumptions

  • The acceleration due to gravity is \(-9.8~m/s^2\).
  • You may neglect rolling friction and drag.
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