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 0.859 rad/s. You, with a mass of 69.3 kg, walk clockwise around the platform along its edge at the speed of 1.03 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 18.9-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 90.5 kg and radius 1.91 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 90.5 kg, radius 1.91 m, 0.859 rad/s
You 69.3 kg, cw 1.03 m/s, at r
Poodle 21.1 kg, cw 1.03/2 m/s, at r/2
Mutt 18.9 kg, 3r/4

You

Relative
= v/r
= 1.03/1.91
= 0.539
Actual
= 0.859 - 0.539
= 0.32
I = mr^2
= 69.5*1.91^2
= 252.81
L = I
= 252.81*0.32
= 80.9

Poodle

Relative
= (1.03/2)/(1.91/2)
= 0.4918
Actual
= 0.859 - 0.4918
= 0.3672

I = m(r/2)^2
= 21.1*(1.91/2)^2
= 19.24
L = I
= 19.24*0.3672
= 7.06

Mutt

Actual
= 0.859
I = m(3r/4)^2
= 18.9(3*1.91/4)^2
= 38.78
L = I
= 38.78*0.859
= 33.31

Disk

I = mr^2/2
= 90.5(1.91)^2/2
= 165.07
L = I
= 165.07*0.859
= 141.79

Total
L = 80.9 + 7.06 + 33.31 + 141.79
= 263.06 kg m^2/s

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