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 0.905 rad/s. You, with a mass of 68.3 kg, walk clockwise around the platform along its edge at the speed of 1.07 m/s with respect to the platform. Your 20.1-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-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 1.87 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)(1.87)2 I=159.28 kg m^2 L=I=(159.28)(0.905 rad/s) L=144.15 PERSON I=MR2 I=68.3(1.87)2 I=238.83 L=I=(238.83)(0.905-1.07/1.87) (v/r=) L=79.50 POODLE I=MR2 I=20.1(1.87/2)2 I=17.57 L=I=(17.57)(0.905-1.07/1.87) L=5.84 MUTT I=MR2 I=18.3(3/4*1.87)2 I=35.99 L=I=(35.99)(0.905) L=32.57 TOTAL we just sum up all the L we found above Lsystem=144.15+79.50+5.84+32.57 Lsystem=262.066 kg m2/s (counter clockwise)

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