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 0.965 rad/s. You. with a mass of 65.7 kg, walk clockwise around the platform along its edge at the speed of 1.09 m/s with respect to the platform. Your 20.3-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 90.9 kg and radius 1.89 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 90.9 kg, radius 1.89 m, 0.965 rad/s
You 65.7kg, cw 1.09 m/s, at r
Poodle 20.3 kg, cw 1.09/2 m/s, at r/2
Mutt 18.5 kg, 3r/4

You

Relative
= v/r
= 1.09/1.89
= 0.576
Actual
= 0.965 - 0.576
= 0.389

I = mr^2
= 65.7*1.89^2
= 234.68
L = I
= 234.68*0.389
=91.29

Poodle

Relative
= (1.09/2)/(1.89/2)
= 0.576
Actual
= 0.965 - 0.576
= 0.389

I = m(r/2)^2
= 20.3*(1.89/2)^2
= 18.12
L = I
= 18.12*0.389
= 7.05

Mutt

Actual
= 0.965
I = m(3r/4)^2
= 18.5(3*1.89/4)^2
= 37.17
L = I
= 37.17*0.965
= 35.86

Disk

I = mr^2/2
= 90.9(1.89)^2/2
= 162.35
L = I
= 162.35*0.965
= 156.66

Total
L = 91.29 + 7.05 + 35.86 + 156.66
= 290.86 kg m^2/s

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