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 0.805 rad/s. You, with a mass of 72.7 kg, walk clockwise around the platform along its edge at the speed of 1.13 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 18.5-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 90.7 kg and radius 1.93 m. Calculate the total angular momentum of the system Number kg·m"/s

Explanation / Answer

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

L1 = (1/2)*90.7*1.93^2*0.805 = +136 kg m^2 /s

angular momentum of person L2 = m*v1*R

v1 = v + Rw = (-1.13)+(1.93*0.805) = + 0.423 m/s

L2 = +72.7*0.423*1.93 = +119.2 kg m^2 /s

angular momentum of poodle L3 = m*v2*R/2

v2 = v + Rw/2 = -(1.13/2)+((1.93*0.805)/2) = + 0.212 m/s

L3 = +20.1*(0.212)*(1.93/2) = +4.11 kg m^2 /s

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

L4 = 18.5*((3*1.93/4)^2*0.805) = +31.2 kg m^2 /s

Ltot = L1 L2 + L3 + L4

Ltot = 136 + 119.2 + 4.11 + 31.2

Ltot = 290.5 kg m^2/s

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