Cоmpоsite Rоlling Body аnd Projectile Motion PHY 2048C Cumulаtive Finаl Examination Points: 10 Suggested Time: 25–30 minutes Instructions: Show all work. Begin each derivation with an appropriate fundamental physics principle. Clearly define any additional symbols you introduce. Unsupported answers may not receive full credit. A rigid composite wheel consists of a uniform solid cylinder of mass 2m and radius R rigidly attached to a thin hoop of mass m and radius R. The wheel starts from rest at a vertical height H above the end of a track. It rolls without slipping down the track and leaves the track horizontally from the edge of a platform that is a height h above the floor. Neglect rolling resistance and air resistance. Reference Information Isolid cylinder = (1/2)MR2, Ithin hoop = MR2 Tasks Part A. Determine the total moment of inertia of the composite wheel about its central axis. Part B. Using conservation of mechanical energy, derive the translational speed v of the wheel's center of mass as it leaves the track. Part C. Determine the angular speed ω of the wheel at the edge of the platform. Part D. Determine the horizontal distance x from the edge of the platform to the point where the wheel first contacts the floor. Treat the wheel's center of mass as the projectile point for this calculation. Part E. Determine the fraction of the wheel's total kinetic energy that is rotational immediately before it leaves the track. Explain whether this fraction depends on H.
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