A circular platform of radius R p = 3.49 m and mass M p = 335 kg rotates on fric

Question

A circular platform of radius Rp = 3.49 m and mass Mp = 335 kg rotates on frictionless air bearings about its vertical axis at 4.13 rpm. An 86.1-kg man standing at the very center of the platform starts walking (at t = 0) radially outward at a speed of 0.543 m/s with respect to the platform. Approximating the man by a vertical cylinder of radius Rm = 0.215 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

I = 1/2 Mp Rp^2 + 1/2 Mm Rm^2 + Mm x^2 moment if inerta
Rm = radius of man, x = distance of man from center
I0 w0 = I w conservation of angular momentum
Since x = v t where v is walking speed of man
I0 w0 = (1/2 Mp Rp^2 + 1/2 Mm Rm^2 + Mm * (v t)^2) w
Solve for angular velocity w

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