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 0.941 rad/s. You, with a mass of 67.9 kg, walk clockwise around the platform along its edge at the speed of 1.05 m/s with respect to the platform. Your 20.1-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 17.3-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 90.7 kg and radius 1.83 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 90.7 kg, radius 1.83 m, 0.941 rad/s
You 67.9 kg, cw 1.05 m/s, at r
Poodle 20.1g, cw 1.05/2 m/s, at r/2
Mutt 17.3 kg, 3r/4

You

Relative
= v/r
= 1.05/1.83
= 0.5737
Actual
= 0.941 - 0.573
= 0.368

I = mr^2
= 67.9*1.83^2
= 227.39
L = I
= 227.39*0.368
= 83.67

Poodle

Relative
= (1.05/2)/(1.83/2)
= 0.573
Actual
= 0.941 - 0.573
= 0.368

I = m(r/2)^2
= 20.1*(1.83/2)^2
= 16.82
L = I
= 16.82*0.368
=6.18

Mutt

Actual
= 0.941
I = m(3r/4)^2
= 17.3(3*1.83/4)^2
= 32.58
L = I
= 32.58*0.941
= 30.65

Disk

I = mr^2/2
= 90.7(1.83)^2/2
= 151.87
L = I
= 151.87*0.941
= 142.90

Total
L = 83.67  + 6.18 + 30.65 + 142.90  
= 263.4 kg m^2/s

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