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 0.947 rad/s. You, with a mass of 67.3 kg, walk clockwise around the platform along its edge at the speed of 1.09 m/s with respect to the platform. Your 20.3-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 92.7 kg and radius 1.83 m. Calculate the total angular momentum of the system.

Explanation / Answer

you

relative w = v/r = 1.09/1.83 = 0.5956 rad/s

actual = 0.947 - 0.5956 = 0.35137 rad

I = mr^2 = 67.3 * 1.83^2 =225.38 kg-m^2

L = Iw = 79.192

for poodle

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

actual = 0.35137 rad

I = m(r/2)^2

L = 5.972

for mutt

w = 0.947

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

L = Iw

L = 33.36

for disk

I = mr^2/2

w = 0.947

L = Iw

L = 146.9947 = 147

total

L = 265.52 kg-m^2/s

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