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 0.929 rad/s. You, with a mass of 75.1 kg, walk clockwise around the platform along its edge at the speed of 1.05 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 18.7-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 1.83 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given
Circular platform rotates ccw 90.9 kg, radius 1.83 m, 0.929 rad/s
You 75.1 kg, cw 1.05 m/s, at r
Poodle 21.1 kg, cw 1.05/2 m/s, at r/2
Mutt 18.7 kg, 3r/4

You
Relative
? = v/r
= 1.05/1.83
= 0.5737
Actual
? = 0.929 - 0.5733
= 0.355

I = mr^2
= 75.1*1.83^2
= 251.50
L = I?
= 251.5*0.355
= 89.23

Poodle

Relative
? = (1.05/2)/(1.83/2)
= 0.480
Actual
? = 0.929 - 0.480
= 0.449

I = m(r/2)^2
= 21.1*(1.83/2)^2
= 17.66
L = I?
= 17.66*0.449
= 7.93

Mutt

Actual
? = 0.929
I = m(3r/4)^2
= 18.7(3*1.83/4)^2
= 35.22
L = I?
= 35.22*0.929
= 32.71

Disk

I = mr^2/2
= 90.9(1.83)^2/2
= 152.20
L = I?
= 152.17*0.929
= 141.40

Total
L = 89.23 + 7.93 + 32.71 + 141.40
= 271.29 kg m^2/s

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