Sapling Learning A horizontal circular platform rotates counterclockwise about i

Question

Sapling Learning A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.983 rad/s. You, with a mass of 69.9 kg, walk clockwise around the platform along its edge at the speed of 1.15 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 atform's radius and at half your linear speed with respect to the platform. Your 17.7-kg mutt, on the other nd, sits still on the platform at a position that is 3/4 of the platform's radius from the center. Model the latform as a uniform disk with mass 91.7 kg and radius 1.87 m. Calculate the total angular momentum of e system. Number kg.ms

Explanation / Answer

Given

Circular platform rotates ccw 91.7 kg, radius 1.87 m, 0.983 rad/s
You 69.9 kg, cw 1.15 m/s, at r
Poodle 2. kg, cw 1.15/2 m/s, at r/2
Mutt 17.7 kg, 3r/4

You

Relative
= v/r
= 1.15/1.87
= 0.6149
Actual
= 0.983 - 0.6149
= 0.3681

I = mr^2
= 69.9*1.87^2
= 244.43
L = I
= 244.43*0.3681
= 89.975

Poodle

Relative
= (1.15/2)/(1.87/2)
= 0.5376
Actual
= 0.983 - 0.5376
= 0.4454

I = m(r/2)^2
= 21.1*(1.87/2)^2
= 18.44
L = I
= 18.44*0.3681
= 6.79

Mutt

Actual
= 0.983
I = m(3r/4)^2
= 17.7(3*1.87/4)^2
= 34.816
L = I
= 34.816*0.983
= 34.22

Disk

I = mr^2/2
= 91.7(1.87)^2/2
= 80.166
L = I
= 80.166*0.983
= 78.80

Total
L = 89.975 + 6.79 + 34.22 + 78.80

= 209.78 kg m^2/s

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