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 0.833 rad/s. You, with a mass of 68.9 kg, walk clockwise around the platform along its edge at the speed of 1.19 m/s with respect to the platform. Your 20.5-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 17.9-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 92.7 kg and radius 1.89 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 92.7 kg, radius 1.89 m, 0.833 rad/s
You 68.9 kg, cw 1.19 m/s, at r
Poodle 20.5 kg, cw 1.19/2 m/s, at r/2
Mutt 17.9 kg, 3r/4

You

Relative
= v/r
= 1.19/1.89
= 0.6296
Actual
= 0.833 - 0.6296
= 0.2034

I = mr^2
= 68.9*1.89^2
= 246.12
L = I
= 246.12*0.2034
= 50.06

Poodle

Relative
= (1.19/2)/(1.89/2)
= 0.6296
Actual
= 0.833 - 0.6296
= 0.2034

I = m(r/2)^2
= 20.5*(1.89/2)^2
= 18.31 kgm^2
L = I
= 18.31*0.2034
= 3.72

Mutt

Actual
= 0.833
I = m(3r/4)^2
= 17.9(3*1.89/4)^2
= 35.97
L = I
= 35.97*0.833
= 29.96

Disk

I = mr^2/2
= 92.7(1.89)^2/2
= 165.57
L = I
= 165.57*0.833
= 137.92

Total
L = 50.06 + 3.72 + 29.96 + 137.92
= 221.66 kg m^2/s

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