A circular platform of radius Rp = 2.99 m and mass Mp = 373 kg rotates on fricti

Question

A circular platform of radius Rp = 2.99 m and mass Mp = 373 kg rotates on frictionless air bearings about its vertical axis at 6.55 rpm. An 70.5-kg man standing at the very center of the platform starts walking (at t = 0) radially outward at a speed of 0.323 m/s with respect to the platform. Approximating the man by a vertical cylinder of radius Rm = 0.241 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

The MoI of the platform+man is
I = 0.5*Mp*Rp^2 + Mm*Rm^2
and, in turn, Rm = Vm*t
where Mm, Rm and Vm are, respectively, the man's Mass, Radius and Velocity.
Plugging in values, find
I = 0.5* 373kg * (2.99m)^2 + 70.5kg * (0.323m/s * t)^2
I = 1667.32865kg

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