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**help help help....please.....rotational motion**

these dang problems keep gettin me//// 20 kg girl on a turntable 4m from center... the turntable has a moment of inertia = 200kgm^2. assume the girl is a point mass. assume the girl and the turn table are rotating at 1 rad/sec. if the girl walks inward to a radius of 3 m, what is the new angular velocity of the girl and the turntable.....

ok so here is my work and once again i dont know what i did wrong.......

I=200

at radius 4m Ipm= .5(20)(4)^2 = 160 so at radius 4 the turntable and the girl have inertia = 360

ok and now for radius 3 m .5(20)(3)^2= 90 so at radius 3m turntable and girl have inertia =290 sooooo then i used MEi = MEf

.5(360)(1)^2 = .5(290)(omega)^2 giving me an angular velocity of 1.12rad per sec.......alas the answer is 1.37 and thats where im stuck

.... i feel the part im missing is when the girl is walking in,,,, im thinking of using Wnet=deltaKE by doing this i get total work done is (1) (Vsq)/r which i get to equal 4J... however i equated this at radius 4m..... im sure i could use MEi = MEf,,,,, im just frustrated right now, so im trying everything.... i guess im just confused how you account for the girl walking in toward the center WHILE its turning.....thank you a ton for anyone who can help me///