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 0.845 rad/s. You, with a mass of 65.7 kg, walk clockwise around the platform along its edge at the speed of 1.19 m/s with respect to the platform. Your 20.9-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 17.7-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 90.9 kg and radius 1.81 m. Calculate the total angular momentum of the system.

Explanation / Answer

angular speed of the platform, w = 0.85 rad/s

angular momentum of platform , Lp = I * w

Lp = 0.5 * 90.9 * 1.81^2 * 0.85

Lp = 125.6 Kg.m^2

angular momentum of person , Lp1 = 65.7 * 1.81^2 * (0.845 - 1.19/1.81 )

angular momentum of poodle , Lp2 = 20.9 * (1.81/2)^2 * (0.845 - 2 * (1.19/2)/1.81 )

angular momentum of mutt , Lp3 = (3/4 * 1.81)^2 * 17.7 * 0.845

For the total angular momentum

total angular momentum = 125.6 + 65.7 * 1.81^2 * (0.845 - 1.19/1.81 ) + 20.9 * (1.81/2)^2 * (0.845 - 2 * (1.19/2)/1.81 ) + (3/4 * 1.81)^2 * 17.7 * 0.845

total angular momentum = 196.73 Kg.m^2

the total angular momentum is 196.73 Kg.m^2

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