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 0.935 rad/s. You, with a mass of 66.9 kg, walk clockwise around the platform along its edge at the speed of 1.17 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 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 91.1 kg and radius 1.95 m. Calculate the total angular momentum of the system.

Explanation / Answer

angular momentum is the product of moment of inertia and angular speed. For the problem we just need to sum of the angular moment of each object.

PLATFORM
I=(1/2)MR2

I=(1/2)(91.1)(1.95)2

I=173.2

L=I=(173.2)(.935)

L=161.95
PERSON
I=MR2

I=66.9(1.95)2

I=254.4

L=I=(254.4)(.935-1.17/1.95)

L=85.22
POODLE

I=MR2

I=20.3(1.95/2)2

I=19.3

L=I=(19.3)(.935-1.17/1.95)

L=6.46

MUTT

I=MR2

I=17.9(3/4*1.95)2

I=38.3

L=I=(38.3)(.935)

L=35.80

TOTAL

we just sum up all the L we found above

Lsystem=161.95+85.22+6.46+35.80

Lsystem=2893.43 kg m2/s (counter clockwise)

Hope that helps

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