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 0.923 rad/s. You, with a mass of 68.5 kg, walk clockwise around the platform along its edge at the speed of 1.11 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 17.7-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 92.5 kg and radius 1.89 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 92.5 kg, radius 1.89 m, 0.923 rad/s
You 68.5 kg, cw 1.11 m/s, at r
Poodle 20.1 kg, cw 1.11/2 m/s, at r/2
Mutt 17.7 kg, 3r/4

You

Relative
= v/r
= 1.11/1.89
= 0.5873
Actual
= 0.923 - 0.5873
= 0.3356

I = mr^2
= 68.5*1.89^2
= 244.68
L = I
= 244.68*0.3356
= 82.11

Poodle

Relative
= (1.11/2)/(1.89/2)
= 0.5244
Actual
= 0.923 - 0.5244
= 0.3985

I = m(r/2)^2
= 20.1*(1.89/2)^2
= 17.94
L = I
= 17.94*0.3985
= 7.15

Mutt

Actual
= 0.923
I = m(3r/4)^2
= 17.7(3*1.89/4)^2
= 35.56
L = I
= 35.56*0.923
= 32.82

Disk

I = mr^2/2
= 92.5(1.89)^2/2
= 165.20
L = I
= 165.20*0.923
= 152.48

Total
L = 82.11 + 7.15 + 32.82 + 152.48
= 274.56 kg m^2/s

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