Question

A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.977 rad/s. You, with a mass of 73.3 kg, walk clockwise around the platform along its edge at the speed of 1.09 m/s with respect to the platform. Your 21.1-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 18.5-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 90.5 kg and radius 1.87 m. Calculate the total angular momentum of the system.

Answer 1

Given data:

You 73.3 kg, clockwise 1.09 m/s, at the position, r
Poodle 21.1 kg, cw 1.09/2 m/s, at the position, r/2
Mutt 18.5 kg,at the position, 3r/4

You : Relative angular speed

ω = v/r = 1.09/1.87 = 0.58288

Therefore, the actual speed

ω = 0.977 rad/s - 0.58288 rad/s = 0.394

Moment of inerita: I = mr^2 = 73.3 x 1.87^2 = 256.32

Therefore, the angular momentum : L = Iω = (256.32) ( 0.394) = 101 kg-m ²/sec

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Relative angualr speed of Poodle

ω = (1.09/2)/(1.87/2) =0.58288

Therefore, the actual speed :

ω = 0.977 rad/s - 0.58288 rad/s = 0.394

Moment of inetia: I = m(r/2)^2 = 21.1*(1.87/2)^2 = 18.44

Therefore, the angular momentum: L = Iω = 18.44 x 0.394 = 7.269 kg-m ²/sec

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Relative angualr speed of Mutt

ω = 0.977

Moment of inertia: I = m(3r/4)^2 = 18.5 (3*1.87/4)^2 = 36.389

Angular momentum: L = Iω = (36.389) ( 0.977 ) = 35.55

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Moment of inerita of Disk , I = mr^2/2 = 90.5 kg x (1.87)^2/2 = 158.234

Angular momentum: L = Iω = ( 158.234 ) (0.977 ) = 154.59

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Total angular mometum is sum of all above momenta

L = 101 + 7.269 + 35.55 + 154.59 = 298.4 kg m^2/s