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 0.807 rad/s. You, with a mass of 72.7 kg, walk clockwise around the platform along its edge at the speed of 1.11 m/s with respect to the platform. Your 20.7-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 18.9-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 91.9 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)*91.9*1.87*1.87*0.807 = +129.67 kg m^2 /s

v1 = v + Rw = (-1.11)+(0.807*1.87) = + 0.399 m/s

angular momentum of person L2 = m*v1*R

L2 = +72.7*0.399*1.87 = +54.243651 kg m^2 /s

v2 = v + 3Rw/4 = -(1.11/2)+((3*1.87*0.807)/4) =+ 0.5768 m/s

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

L3 = +20.7*(0.5768)*(1.87/2) = +11.1636 kg m^2 /s

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

L4 = +18.9*(1.4025*1.4025*0.807) = +30.00 kg m^2 /s

Ltot = L1 L2 + L3 + L4 = 129.67 +54.243651 + 11.1636 + 30.00 = +225.077251 kg m^2/s

counter clock wise direction

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