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 0.849 rad/s. You, with a mass of 74.7 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 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 92.5 kg and radius 1.81 m. Calculate the total angular momentum of the system.

Explanation / Answer

Circular platform rotates ccw 74.7 kg, radius 1.81 m, 0.849 rad/s
You 71.5 kg, cw 1.09 m/s, at r
Poodle 20.3 kg, cw 1.09/2 m/s, at r/2
Mutt 17.5 kg, 3r/4

You

Relative
= v/r
= 1.09/1.81
= 0.6022
Actual
= 0.849 - 0.6022
= 0.78878

I = mr^2
= 74.7*1.81^2
= 244.72
L = I
= 244.72*0.78878
= 193.03

Poodle

Relative
= (1.09/2)/(1.81/2)
= 0.6022
Actual
= 0.849- 0.6022
= 0.2468

I = m(r/2)^2
= 20.3*(1.81/2)^2
= 16.63
L = I
= 16.63*0.2468
= 4.13

Mutt

Actual
= 0.849
I = m(3r/4)^2
= 17.5(3*1.81/4)^2
= 32.25
L = I
= 32.25*0.849

=27.38

Disk

I = mr^2/2
= 92.5(1.81)^2/2
= 151.52
L = I
= 151.52*0.849
= 128.64

Total
L = 193.03+ 4.13 + 27.38 + 128.64
= 353.18 kg m^2/s

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