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

I1 = Mp*Rp^2 + 0.5*Mm*Rm^2 ......W1 = 4.13rpm

I2 = Mp*Rp^2 + 0.5*Mm*Rm^2+Mm*Rp^2......W2 = ?

I1*W1 = I2*W2

(Mp*Rp^2 + 0.5*Mm*Rm^2)*W1 = (Mp*Rp^2 + 0.5*Mm*Rm^2+Mm*Rp^2)*W2


((335*3.29^2)+(0.5*86.1*0.215^2))*4.13 = ((335*3.29^2)+(0.5*86.1*0.215^2)+(86.1*3.49^2))*W2

W2 = 3.203 rpm

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