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 0.973 rad/s. You, with a mass of 73.3 kg, walk clockwise around the platform along its edge at the speed of 1.07 m/s with respect to the platform. Your 20.7-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 17.5-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 92.1 kg and radius 1.97 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 92.1 kg, radius 1.97 m, 0.973 rad/s
You 73.3 kg, cw 1.07 m/s, at r
Poodle 20.7 kg, cw 1.07/2 m/s, at r/2
Mutt 17.5 kg, 3r/4

You

Relative
= v/r
= 1.07/1.97
= 0.543
Actual
= 0.973 - 0.543
= 0.429

I = mr^2
= 73.3*1.97^2
= 284.46
L = I
= 284.46*0.429
= 122.033

Poodle

Relative
= (1.07/2)/(1.97/2)
= 0.5269
Actual
= 0.973 - 0.5269
= 0.4460

I = m(r/2)^2
= 20.7*(1.97/2)^2
= 20.08
L = I
= 20.08*0.4460
= 8.9573

Mutt

Actual
= 0.973
I = m(3r/4)^2
= 17.5(3*1.97/4)^2
= 38.20
L = I
= 38.20*0.973
= 37.171

Disk

I = mr^2/2
= 92.1(1.97)^2/2
= 178.71
L = I
= 178.71*0.973
= 173.89

Total
L = 122.033  +8.9573 + 37.171 + 173.89
= 342.05 kg m^2/s

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