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 0.887 rad/s. You, with a mass of 70.5 kg, walk clockwise around the platform along its edge at the speed of 1.07 m/s with respect to the platform. Your 21.1-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 18.5-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 92.7 kg and radius 1.85 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 92.7 kg, radius 1.85 m, 0.887 rad/s
You 70.5 kg, cw 1.07 m/s, at r
Poodle 21.1 kg, cw 1.07/2 m/s, at r/2
Mutt 18.5 kg, 3r/4

You

Relative
? = v/r
= 1.07/1.85
= 0.578
Actual
? = 0.887 - 0.578
= 0.3086

I = mr^2
= 70.5*1.85^2
= 241.29
L = I?
= 241.29*0.3086
= 74.46

Poodle

Relative
? = (1.07/2)/(1.85/2)
= 0.5784
Actual
? = 0.887 -0.5784
= 0.3086

I = m(r/2)^2
= 21.1*(1.85/2)^2
= 18.54
L = I?
= 18.54*0.3086
= 5.57

Mutt

Actual
? = 0.887
I = m(3r/4)^2
= 18.5(3*1.85/4)^2
= 35.62
L = I?
= 35.62*0.887
= 31.59

Disk

I = mr^2/2
= 92.7(1.85)^2/2
= 158.63
L = I?
= 158.98*0.887
= 140.71

Total
L = 252.33kg m^2/s

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