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 0.897 rad/s. You, with a mass of 69.7 kg, walk clockwise around the platform along its edge at the speed of 1.19 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 18.7-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 1.89 m. Calculate the total angular momentum of the system.

Explanation / Answer

Here,

w1 = 0.897 rad/s

m1 = 69.7 Kg

v1 = 1.19 m/s

Total angular momentum of the system = angular momentum of platform + angular momentum of person + angular momentum of poodle + angular momentum of mutt

Total angular momentum of the system = 0.5 * 90.5 * 1.89^2 * 0.897 + 69.7 * 1.89 * (0.897 * 1.89 - 1.19) + 20.7 * (1.90/2) * (0.897 * 1.89 - 1.19)/2 + 18.7 * (3/4 * 1.89)^2 * 0.897

calculating

Total angular momentum of the system = 250.23 Kg.m^2

the Total angular momentum of the system is 250.23 Kg.m^2

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