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 0.979 rad/s. You, with a mass of 70.3 kg, walk clockwise around the platform along its edge at the speed of 1.11 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 18.5-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 1.81 m. Calculate the total angular momentum of the system.

Explanation / Answer

I=(1/2)MR^2 =(1/2)(90.9)(1.81)^2= I=148.9

L=Iw=(148.9)(0.979) =145.77 PERSON

I=MR^2=70.3* 1.81*1.81=230.31
L=Iw=(230.31)(0.909-1.1/1.81) (v/r=w)
L=24.30
POODLE
I=MR2 =20.3(1.81/2)^2 =16.62
L=Iw=(16.62)(0.909-1.11/1.95) =1.713
MUTT
I=MR2
I=18.5 (3/4*1.81)^2 = 34.1
L=Iw=(34.1)(0.909)
L=30.98

TOTAL =145.77+24+1.713+30.98 = 202.463 kg m2/s (counter clockwise)

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