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 0.939 rad/s. You, with a mass of 67.9 kg, walk clockwise around the platform along its edge at the speed of 1.01 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 17.3-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 91.5 kg and radius 1.89 m. Calculate the total angular momentum of the system.

Explanation / Answer

You

Relative
? = v/r
= 1.01/1.89
= 0.5343

Actual
? = 0.939- 0.5343

= 0.4046

I = mr^2
= 67.9*1.89^2
=242.54

L = I?
= 242.54*0.4046
= 98.1339

Poodle

Relative
? = (1.01/2)/(1.89/2)
= 0.5343
Actual
? = 0.939 - 0.5343
= 0.4046

I = m(r/2)^2
= 20.3*(1.81/2)^2
= 18.1284

L = I?
= 18.1284*0.4046
=7.334

Mutt

Actual
? = 0.943
I = m(3r/4)^2
= 17.3(3*1.89/4)^2
= 34.76
L = I?
= 34.76*0.939
= 32.64

Disk

I = mr^2/2
= 91.5(1.89)^2/2
= 163.423
L = I?
= 163.423*0.939
= 153.454


Total

L = 98.1339+7.334+32.64+153.454

=291.56

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