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 0.889 rad/s. You, with a mass of 73.1 kg, walk clockwise around the platform along its edge at the speed of 1.11 m/s with respect to the platform. Your 20.9-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 92.1 kg and radius 1.93 m. Calculate the total angular momentum of the system.

Explanation / Answer

L = I + mvr
L = ½*92.1kg*(1.93m)²*0.889rad/s
+ 73.1kg*(0.889rad/s*1.93m - 1.11m/s)*1.93m
+ 20.9kg*(0.889rad/s*1.93m / 2 - 1.11m/s / 2)*(1.93m / 2)
+ 17.5kg*(3*1.93m / 4)²*0.889rad/s
L = 276.66 kg·m²/s

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