A circular platform of radius R p = 5.37 m and mass M p = 371 kg rotates on fric

Question

A circular platform of radius Rp = 5.37 m and mass Mp = 371 kg rotates on frictionless air bearings about its vertical axis at 7.25 rpm. An 76.7-kg man standing at the very center of the platform starts walking (at t = 0) radially outward at a speed of 0.563 m/s with respect to the platform. Approximating the man by a vertical cylinder of radius Rm = 0.237 m, determine an equation (specific expression) for the angular velocity of the platform as a function of time. What is the angular velocity when the man reaches the edge of the platform?

Explanation / Answer

apply the conservation of angular momentum
w = angular velocity
I stands for Inertia
I1w1 = I2w2
so Inertia 1 times angular velocity 1 equals Inertia 2 times angular velocity 2

When the person walks to the edge, they have a moment of inertia due to a point mass
I = mr2  

the total moment of inertia after they walk to the edge is
I2  

I1w1 = I2w2
the angular velocity when the person reaches the edge is rad/s

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