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 0.993 rad/s. You, with a mass of 72.9 kg, walk clockwise around the platform along its edge at the speed of 1.13 m/s with respect to the platform. Your 20.5-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 18.7-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 90.5 kg and radius 1.97 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)*90.5*1.97^2*0.993 = +174.38 kg m^2 /s

angular momentum of person L2 = m*v1*R

v1 = v + Rw = (-1.13)+(0.993*1.97) = + 0.83 m/s

L2 = +72.9*0.83*1.97 = +119.2 kg m^2 /s

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

v2 = v + Rw/2 = -(1.13/2)+((1.97*0.937)/2) = + 0.36 m/s

L3 = +20.5*(0.36)*(1.97/2) = +7.27 kg m^2 /s

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

L4 = +18.7*((3*1.97/4)*0.993) = +27.43 kg m^2 /s

Ltot = L1 L2 + L3 + L4 = +174.38 +119.2 + 7.27 +27.43 = +328.3 kg m^2/s

counter clock wise direction

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