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 0.839 rad/s. You, with a mass of 70.9 kg, walk clockwise around the platform along its edge at the speed of 1.01 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 17.5-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 92.7 kg and radius 1.93 m. Calculate the total angular momentum of the system.

Explanation / Answer

moment ofinertia of the disk is I1 = 0.5*M*R^2 = 0.5*92.7*1.93*1.93 = 172.64 kg-m^2

angular speed is w1 = 0.839 rad/s

moment of inertia of person is I2 = m*r^2 = 70.9*1.93*1.93 = 264.1 kg-m^2

w2 = v/r = 1.01/1.93 = 0.523 rad/s

I_poodle = 21.1*(1.93/2)^2 = 19.64 kg-m^2

w_poodle = 0.523 rad/s

I_mutt = 17.5*(3/4)^2*1.93*1.93 = 36.67 kg-m^2

w-mutt = 0.839 rad/s

then total angular momentum of the system is L = (I1*w1)-(I2*w2)-(I_poodle*w_poodle) + (I_mutt*w_mutt)

L = (172.64*0.839)-(264.1*0.523)-(19.64*0.523)+(36.67*0.839) = 27.21 kg*m^2/s

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