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 0.863 rad/s. You, with a mass of 72.1 kg, walk clockwise around the platform along its edge at the speed of 1.17 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 18.1-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 91.9 kg and radius 1.95 m. Calculate the total angular momentum of the system.

Explanation / Answer

you

relative w = v/r = 1.17/1.95 = 0.6 rad/s

actual = 0.863 - 0.6 = 0.263 rad

I = mr^2 = 72.1 * 1.95^2 =274.16 kg-m^2

L = Iw = 72.1

for poodle

w = (v/2)/(r/2)

actual = 0.263 rad

I = m(r/2)^2

L = 5.125

for mutt

w = 0.863

I = m*(3r/4)^2

L = Iw

L = 33.4

for disk

I = mr^2/2

w = 0.863

L = Iw

L = 150.79

total

L = 261.412567 kg-m^2/s

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