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 0.869 rad/s. You, with a mass of 68.3 kg, walk clockwise around the platform along its edge at the speed of 1.05 m/s with respect to the platform. Your 20.9-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 17.1-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 90.3 kg and radius 1.93 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 90.3 kg, radius 1.93 m, 0.869 rad/s
You 68.3 kg, cw 1.05 m/s, at r
Poodle 20.9 kg, cw 1.05/2 m/s, at r/2
Mutt 17.1 kg, 3r/4

You

Relative
? = v/r
= 1.05/1.93
= 0.5444
Actual
? = 0.869 - 0.6022
= 0.325

I = mr^2
= 68.3*1.93^2
= 254.41
L = I?
= 254.41*0.325
= 82.6

Poodle

Relative
? = (1.05/2)/(1.93/2)
= 0.777
Actual
? = 0.869 - 0.777
= 0.091

I = m(r/2)^2
= 20.9*(1.93/2)^2
= 19.46
L = I?
= 19.46*0.091
= 1.77

Mutt

Actual
? = 0.869
I = m(3r/4)^2
= 17.1(3*1.93/4)^2
= 35.82
L = I?
= 35.82*0.869
= 31.13

Disk

I = mr^2/2
= 90.3(1.93)^2/2
= 168.17
L = I?
= 168.17*0.869
= 146.14

Total
L = 82.6 + 1.77 + 31.13 + 146.14
= 261.64 kg m^2/s

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