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 0.855 rad/s. You, with a mass of 74.3 kg, walk clockwise around the platform along its edge at the speed of 1.11 m/s with respect to the platform. Your 20.5-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 17.7-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 93.1 kg and radius 1.97 m. Calculate the total angular momentum of the system.

_____ kg*m^2/s

Explanation / Answer

Given

Circular platform rotates ccw 93.1 kg, radius 1.97 m, 0.855 rad/s
You 74.3 kg, cw 1.11 m/s, at r
Poodle 20.5 kg, cw 1.11/2 m/s, at r/2
Mutt 17.7 kg, 3r/4

You

Relative
= v/r
= 1.11/1.97
= 0.563
Actual
= 0.855 - 0.563
= 0.292

I = mr^2
= 74.3*1.97^2
= 288.35
L = I
= 288.35*.292
= 84.19

Poodle

Relative
= (1.11/2)/(1.97/2)
= 0.5466
Actual
= 0.855 - 0.5466
= 0.3084

I = m(r/2)^2
= 20.5*(1.97/2)^2
= 19.88
L = I
= 19.88*0.3084
= 6.13

Mutt

Actual
= 0.855
I = m(3r/4)^2
= 17.7(3*1.97/4)^2
= 38.63
L = I
= 38.63*0.855
= 33.03

Disk

I = mr^2/2
= 93.1(1.97)^2/2
= 180.65
L = I
= 180.65*0.855
= 154.46

Total
L = 154.46 + 33.03 + 6.13 + 84.19
= 277.81 kg m^2/s

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