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 65.3 kg, walk clockwise around the platform along its edge at the speed of 1.05 m/s with respect to the platform. Your 21.1-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 19.1-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 92.3 kg and radius 1.87 m. Calculate the total angular momentum of the system.

Explanation / Answer

total angular momentum= Iw+sigma(mvr)

I = 92.3*1.87^2/2

so

total angular momentum=[92.3*1.87^2/2*0.913]+[65.3*(0.913*1.87-1.05)*1.87]+[21.1*((0.913*1.87-1.05)/2)*1.87/2]+[19.1*0.913*(1.87*3/4)^2]

= 268.39 kg.m^2/s

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