A 50 kg person stands at the edge of a 7.4 m diameter circular platform, which i

Question

A 50 kg person stands at the edge of a 7.4 m diameter circular platform, which is mounted horizontally on frictionless bearings and has a total mass of 300 kg. The platform is at rest initially, but when the person begins running at a speed of 10 m/s (with respect to the platform) around its edge, the platform begins to rotate in the opposite direction. What is the magnitude of the speed of the person (in m/s) with respect to the ground? You can model the platform as a circular disk.

The answer is NOT 8.33. Thanks for any help.

Explanation / Answer

angular velocity of the person 1=v/r=10/3.7=2.70rad/s

moment of inertia I1=mr2 =50*3.7*3.7=684.5kg-m2

moment of inertia of the discI2=0.5mr2 =0.5*300*3.7*3.7=2053.5kg-m2

2=I11/I2=684.5*2.70/2053.5=0.900rad/s

v2=r2=3.7*0.900=3.33m/s

velocity of the person woth respect to ground=v=v1-v2=10.3.33=06.66m/s

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