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 0.877 rad/s. You, with a mass of 72.7 kg, walk clockwise around the platform along its edge at the speed of 1.13 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 18.1-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 92.1 kg and radius 1.95 m. Calculate the total angular momentum of the system.

Explanation / Answer

L = I + mvr
L = ½*92.1kg*(1.95m)²*0.877rad/s
+ 72.7kg*(0.877rad/s*1.95m - 1.13m/s)*1.95m
+ 21.1kg*(0.877rad/s*1.95m / 2 - 1.13m/s / 2)*(1.95m / 2)
+ 21.1kg*(3*1.95m / 4)²*0.877rad/s

=153.6+82.24+20.57+39.6
L = 296.1 kg·m²/s

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