A person of mass 85 kg stands at the centerof a rotating merry-go-round platform

Question

   A person of mass 85 kg stands at the centerof a rotating merry-go-round platform of radius 4.5 m and moment ofinertia 1050 kg m^2. The platform rotates without frictionwith angular velocity 1.08 rad/s. The person walks radiallyto the edge of teh platform A) Calculate the angular velocity when the personreaches the edge B) Calculate teh rotational kinetic energy of the systemof platform plus person before and after the person's walk Please show all steps    A person of mass 85 kg stands at the centerof a rotating merry-go-round platform of radius 4.5 m and moment ofinertia 1050 kg m^2. The platform rotates without frictionwith angular velocity 1.08 rad/s. The person walks radiallyto the edge of teh platform A) Calculate the angular velocity when the personreaches the edge B) Calculate teh rotational kinetic energy of the systemof platform plus person before and after the person's walk Please show all steps

Explanation / Answer

            Given that the mass of the person is m = 85 kg             The radius of the platform is r = 4.5 m             The moment of inertia of the merry-go-round is I1 = 1050kg.m2             The anglular velocity of the platform is 1 = 1.08 rad/s     --------------------------------------------------------------------------------------            since there is no external torque on the system then the angularmomentum is conserved                                   initial angular momentum = final angular momentum                                                       I1*1 = I2*2                                                         I1*1= (I1+ mr2) *2                                                              2 =  I1*1 / (I1+mr2)                                                                     =----------- rad/s         The intial kineticenergy before walking is K1 = (1/2)I1*12                                                                              =---------- J                    The final kinetic energy after walking is K2 =(1/2)I2*22                                                                           =---------- J                                                                                                    =---------- J                                                                                      =---------- J           

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