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 0.879 rad/s. You, with a mass of 74.1 kg, walk clockwise around the platform along its edge at the speed of 1.05 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 18.7-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 90.3 kg and radius 1.95 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 90.3 kg, radius 1.95 m, 0.879 rad/s
You 74.1 kg, cw 1.05 m/s, at r
Poodle 20.9 kg, cw 1.05/2 m/s, at r/2
Mutt 18.7 kg, 3r/4

You

Relative
= v/r
= 1.05/1.95
= 0.5384
Actual
= 0.879 - 0.5384
= 0.3406

I = mr^2
= 74.1*1.95^2
= 281.76
L = I
= 281.76*0.3406
= 95.96

Poodle

Relative
= (1.05/2)/(1.95/2)
= 0.5384
Actual
= 0.879 - 0.5384
= 0.3406

I = m(r/2)^2
= 20.9*(1.95/2)^2
= 19.86
L = I
= 19.86*0.3406
= 6.76

Mutt

Actual
= 0.879
I = m(3r/4)^2
= 18.7(3*1.95/4)^2
= 39.99
L = I
= 39.99*0.879
= 35.15

Disk

I = mr^2/2
= 90.3(1.95)^2/2
= 171.63
L = I
= 171.63*0.879
= 150.86

Total
L = 95.96 + 6.76 + 35.15 + 150.86
= 288.73 kg m^2/s

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