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 0.965 rad/s. You, with a mass of 66.1 kg, walk clockwise around the platform along its edge at the speed of 1.13 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 18.9-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 91.5 kg and radius 1.97 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 91.5 kg, radius 1.97 m, 0.965 rad/s
You 66.1 kg, cw 1.13 m/s, at r
Poodle 20.3 kg, cw 1.13/2 m/s, at r/2
Mutt 18.9 kg, 3r/4

You

Relative
? = v/r
= 1.13/1.97
= 0.5736
Actual
? = 0.965 - 0.5736
= 0.3914

I = mr^2
= 66.1*1.97^2
= 252.52
L = I?
= 256.52*0.3914
= 100.40

Poodle

Relative
? = (1.13/2)/(1.97/2)
= 0.5565
Actual
? = 0.965 - 0.5565
= 0.4084

I = m(r/2)^2
= 20.3*(1.97/2)^2
= 19.69
L = I?
= 19.69*0.4084
= 8.04

Mutt

Actual
? = 0.965
I = m(3r/4)^2
= 18.9(3*1.97/4)^2
= 41.25
L = I?
= 41.25*0.965
= 39.81

Disk

I = mr^2/2
= 91.5(1.97)^2/2
= 177.55
L = I?
= 177.55*0.965
= 171.33

Total
L = 100.04 + 8.04 + 39.81 + 171.33
= 319.22 kg m^2/s

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