A runner of mass 50.0 runs around the edge of a horizontal turntable mounted on

Question

A runner of mass 50.0 runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude 3.50 . The turntable is rotating in the opposite direction with an angular velocity of magnitude 0.260 relative to the earth. The radius of the turntable is 3.20 , and its moment of inertia about the axis of rotation is 80.0 . Part A Find the final angular velocity of the system if the runner comes to rest relative to the turntable. (You can treat the runner as a particle.)

Explanation / Answer

Relevant equations w=v/r I1w1=I2w2 3. The attempt at a solution okay first we are given the veocity of the runner, to determine his angular velocity its just w1=vrunner/rtable=3.6/3.2=1.125 rad/s I1(runner)=mr^2=51.0*3.2^2=522.24 kg*m^2 now using the conversation of angular momentum I1w1+I2w2=(I1+I2)w2' the w and I provided in the problem statement can be used as w2 & I2 respectivly and we can now solve for w2' which is I1w1+I2w2/(I1+I2)=w2' subbing in all the values (522.24*1.125)+(79.0*0.160)/(522.24+79.0)=600.16/601.24=0.9982=0.988(sig figs) Now the problem I'm having with this is that I still receive an error with this answer and I've been through my work half a dozen times and I dont belive I made any rounding answers so if any one could tell me what Im doing wrong I would be very thankful.

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