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 0.901 rad/s. You, with a mass of 74.1 kg, walk clockwise around the platform along its edge at the speed of 1.11 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 19.1-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 92.7 kg and radius 1.91 m. Calculate the total angular momentum of the system.

Explanation / Answer

Circular platform rotates ccw 92.7 kg, radius 1.91 m, 0.901 rad/s
You 74.1 kg, cw 1.11 m/s, at r
Poodle 20.9 kg, cw 1.11/2 m/s, at r/2
Mutt 19.1 kg, 3r/4

You

Relative
? = v/r
= 1.11/1.91
= 0.5811
Actual
? = 0.901 - 0.5811
= 0.3198

I = mr^2
= 74.1*1.91^2
= 234.24
L = I?
= 270.32*0.3198
= 86.46

Poodle

Relative
? = (1.11/2)/(1.91/2)
= 0.58115
Actual
? = 0.901 - 0.58115
= 0.3198

I = m(r/2)^2
= 20.9*(1.91/2)^2
= 19.06
L = I?
= 19.06*0.3198
= 6.096

Mutt

Actual
? = 0.901
I = m(3r/4)^2
= 19.1(3*1.91/4)^2
= 39.19
L = I?
= 39.19*0.901
= 35.31

Disk

I = mr^2/2
= 92.7(1.91)^2/2
= 169.08
L = I?
= 169.08*0.901
= 152.35

Total
L = 86.46 + 6.096 + 35.31 + 152.35
L = 280.21 kg m^2/s

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