A circular platform of radius Rp = 4.39 m and mass Mp = 467 kg rotates on fricti

Question

A circular platform of radius Rp = 4.39 m and mass Mp = 467 kg rotates on frictionless air bearings about its vertical axis at 5.55 rpm. An 69.7-kg man standing at the very center of the platform starts walking (at t = 0) radially outward at a speed of 0.477 m/s with respect to the platform. Approximating the man by a vertical cylinder of radius Rm = 0.227 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

You know that angular momentum is always conserved. That means that: (Moment of inertia initial)x (angular velocity initial) = (Moment of inertia final) x (angular velocity final) there are two different moments of inertia in this problem. You have the person and the disk. The moment of inertia for the disk is (mr^2)/2 and the person is (mR^2) R=distance the guy is from the center r=radius of the disk plug in the initial values and get the answer note: the equation of angular momentum is both the expression for this problem and also gets you the answer

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