Question

is standing at 3 m from the axis, their angular velocity is 1 rad/s. What would be their angular velocity if the ki moved to the center of the platform? 11. Consider a kid with mass 20 kg standing on a merry-go-round that has rotational inertia of 200 kg m. When t Setup:

Answer 1

Initial Initial angular velocity, w_1^0 = 1 rad/s Initial Momentum of Inertia of child _I I_child = MR^2 = 20 kg times (3m)^2 = 180 kg m^2 Initial Moment of Inertia of Merry-go-round. _I I_MGR = 200 kg m^2 therefore Total Initial Moment of Inertia _I I_Total =_I I_child +_I I_MGR Final Final angular velocity, w_f =? Final Moment of inertia of child _F I_child = MR^2 = 20 times 0 = 0 {as child is in centre. R = 0} Final M.O.I of Merry-go-round _F T_Total =_F I_child +_F I_MGR By conservation of angular moment _I T_Total times w_i =_F I_Total times w_f therefore w_f =_I I_Total times w_i/_F I_Total = 180 + 200/0 + 200 times 1 rad/s w_f = 1.9 rad/s therefore Angular velocity of Merry go-round when Rid moved to centre is w_f = 1.9 rad/s.