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 0.807rad/s. You, with a mass of 73.9 kg, walk clockwise around the platform along its edge at the speed of 1.07 m/s with respect to the platform. Your 20.1-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 17.7-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 92.9 kg and radius 1.87 m. Calculate the total angular momentum of the system.

Explanation / Answer

angular momentum of platform L1 = (1/2)*M*R^2*w

L1 = +(1/2)*92.9*1.87*1.87*0.807 = + 131.082 kg m^2 /s

angular momentum of person L2 = m*v*R

L2 = -73.9*1.07*1.87 = -147.866kg m^2 /s

angular momentum of poodle L3 = m*v*R/2

L3 = -20.1*(1.07/2)*(1.87/2) = -10.0545 kg m^2 /s

angular momentum of mutt L4 = I2*w = m*(3R/4)^2*w

L4 = +17.7*(1.4025*1.4025*0.807) = +28.096 kg m^2 /s

Ltot = L1 L2 + L3 + L4 = 131.082-147.866-10.0545+28.096 = + 1.2575 kg m^2/s

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