A horizontal circular platform rotates counterclockwise about its axis at the ra

Question

A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.913 rad/s. You, with a mass of 70.1 kg, walk clockwise around the platform along its edge at the speed of 1.11 m/s with respect to the platform. Your 20.5-kg poodle also walks clockwise around the platform, but along a circle at half the platform's radius and at half your linear speed with respect to the platform. Your 18.7-kg mutt, on the other hand, sits still on the platform at a position that is 3/4 of the platform's radius from the center. Model the platform as a uniform disk with mass 92.5 kg and radius 1.85 m. Calculate the total angular momentum of the system.

Explanation / Answer

total angular momentum= Iw+sigma(mvr)

I = 92.5*1.85^2/2

so

total angular momentum=[92.5*1.85^2/2*0.913]+[70.1*(0.913*1.85-1.11)*1.85]+[20.5*((0.913*1.85-1.11)/2)*1.85/2]+[18.7*0.913*(1.85*3/4)^2

= 257.97 kg.m^2/s

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