Suppose a 85 kg person stands at the edge ofa 7.5 m diameter merry-go-round turn

Question

   Suppose a 85 kg person stands at the edge ofa 7.5 m diameter merry-go-round turntable that is mounted onfrictionless bearings and has a moment of inertia of 1940 kgm^2. The turntable is at rest initially, but when teh personbegins running at a speed of 3.8 m/s (with respect to theturntable) around its edge, the turntable begins to rotate in theopposite direction. Calculate the angular velocity of the turntable. Please show all steps    Suppose a 85 kg person stands at the edge ofa 7.5 m diameter merry-go-round turntable that is mounted onfrictionless bearings and has a moment of inertia of 1940 kgm^2. The turntable is at rest initially, but when teh personbegins running at a speed of 3.8 m/s (with respect to theturntable) around its edge, the turntable begins to rotate in theopposite direction. Calculate the angular velocity of the turntable. Please show all steps

Explanation / Answer

         Given thatthe mass of the person is m = 85 kg             Thediameter of the platform is d = 7.5 m            The radius of the platform is r = d/2 = 3.75 m             The moment of inertia of the merry-go-round is I1 = 1940kg.m2             The initial angular velocity of the system is 1 = 0              The speed of the person is V = 3.8 m/s     --------------------------------------------------------------------------------------            since there is no external torque on the system then the angularmomentum is conserved                                   initial angular momentum = final angular momentum                                                       I1*1 = angular momentum of platform + person                                                              0 = I1 *2 + mVr                                                             2 = - mVr / I1                                                                     =----------- rad/s               The -ve sign indicates that the motion of the table isopposite to the motion of the person .                       Thediameter of the platform is d = 7.5 m            The radius of the platform is r = d/2 = 3.75 m             The moment of inertia of the merry-go-round is I1 = 1940kg.m2             The initial angular velocity of the system is 1 = 0              The speed of the person is V = 3.8 m/s     --------------------------------------------------------------------------------------            since there is no external torque on the system then the angularmomentum is conserved                                   initial angular momentum = final angular momentum                                                       I1*1 = angular momentum of platform + person                                                              0 = I1 *2 + mVr                                                             2 = - mVr / I1                                                                     =----------- rad/s               The -ve sign indicates that the motion of the table isopposite to the motion of the person .          

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