Question

A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.807 rad/s.0.807 rad/s. You, with a mass of 66.9 kg,66.9 kg, walk clockwise around the platform along its edge at the speed of 1.13 m/s1.13 m/s with respect to the platform. Your 21.1 kg21.1 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 18.3 kg18.3 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 91.3 kg91.3 kg and radius 1.95 m.1.95 m. Calculate the total angular momentum of the system.

Answer 1

Angular momentum = Moment of inertia × Angular speed

Let's calculate angular momentum of each element separately and then add/subtract as per their direction (vectors).

PLATFORM
I=(1/2)MR2
I=(1/2)(91.3)(1.95)2
I=173.584 kgm2
L=Iω=(173.584)(.807)
L=140.08

PERSON
I=MR2
I=66.9(1.95)2
I=254.4
L=Iω=(254.4)(.807-1.13/1.95) (v/r=ω)
L=57.88
POODLE
I=MR2
I=21.1(1.95/2)2
I=20.058
L=Iω=(20.058)(.807-1.13/1.95)
L=4.5634
MUTT
I=MR2
I=18.3(3/4*1.95)2
I=39.14
L=Iω=(39.14)(.807)
L=31.5876

TOTAL
Lsystem=140.08+57.88+4.5634+31.5876
Lsystem=234.11 kg m2/s (counter clockwise)