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 0.969 rad/s. You, with a mass of 74.5 kg, walk clockwise around the platform along its edge at the speed of 1.17 m/s with respect to the platform. Your 21.1-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 18.3-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 92.9 kg and radius 1.83 m. Calculate the total angular momentum of the system.

Explanation / Answer

Circular platform rotates ccw 92.9 kg, radius 1.83 m, 0.969 rad/s
You 74.5 kg, cw 1.17 m/s, at r
Poodle 21.1 kg, cw 1.17/2 m/s, at r/2
Mutt 18.3 kg, 3r/4

You

Relative
= v/r
= 1.17/1.83
= 0.6393
Actual
= 0.969 - 0.6393= 0.3297

I = mr^2
= 74.5*1.83^2
= 252.84
L = I
= 234.24*0.3297
= 83.36
Poodle

Relative
= (1.17/2)/(1.83/2)
= 0.6393
Actual
= 0.969 - 0.6393= 0.3297

I = m(r/2)^2
= 21.1*(1.83/2)^2
= 17.66

L = I
= 17.66*0.3297
= 5.822
Mutt

Actual
= 0.969
I = m(3r/4)^2
= 18.3(3*1.83/4)^2
= 34.47
L = I
= 34.47*0.969
= 33.40

Disk

I = mr^2/2
= 92.9(1.83)^2/2
= 155.55
L = I
= 155.55*0.969
= 150.72

Total
L = 83.36+ 5.822+ 33.40 + 150.72
= 273.30 kg m^2/s

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