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 0.883 rad/s. You, with a mass of 73.1 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 latform's radius and at half your linear speed with respect to the platform. Your 19.1-kg mutt, on the other and, sits still on the platform at a position that is 3/4 of the platform's radius from the center. Model the latform as a uniform disk with mass 90.9 kg and radius 1.93 m. Calculate the total angular momentum of the system Number kg ms In

Explanation / Answer

for a platform, I = 1/2 M R2 = 1/2 * 90.9 * 1.932  = 169.3

L = I w = 169.3 * 0.883 = 149.5

for a person , I = M R2  = 73.1 * 1.932 = 272.3

L = I w = 272.3 * (0.883 - 1.13 / 1.93) = 81.0

for a poodle I = M R2 = 20.5 (1.93/2)2 = 19.1

L = I w = 19.1 *(0.883 - 1.13/1.93) = 5.68

for a mutt I = M R2 = 19.1 (3/4 * 1.93)2 = 40

L = I w = 40 * 0.883 = 35.3

total angular momentum = 149.5 + 81 + 5.68 + 35.3

= 271.5 kg m2/s

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