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 0.843 rad/s. You, with a mass of 71.9 kg, walk clockwise around the platform along its edge at the speed of 1.19 m/s with respect to the platform. Your 20.9-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 17.7-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 90.9 kg and radius 1.87 m. Calculate the total angular momentum of the system.

Explanation / Answer

PLATFORM
I=(1/2)MR2
I=(1/2)(90.9)(1.87)2
I=158.934105

L=Iw=(125.71)(.843)
L=133.981450515

PERSON
I=MR2
I=71.9(1.87)2
I=251.42711

L=Iw=(251.42711)(.843-1.19/1.87) (v/r=w)
L=51.954

POODLE
I=MR2
I=20.9(1.87/2)2
I=18.2713025

L=Iw=(18.27)(.843-1.19/1.87)

L=3.775
MUTT
I=MR2
I=17.7(3/4*1.87)2
I=34.816010625

L=Iw=(34.816)(.843
L=29.349896956875

TOTAL
we just sum up all the L we found above
Lsystem=133.98+51.954+3.775+29.349
Lsystem=219.058896956875kg m2/s (counter clockwise)

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