A horizontal circular platform rotates counterclockwise about its axis at the ra
ID: 2297094 • Letter: A
Question
A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.877 rad/s. You, with a mass of 70.5 kg, walk clockwise around the platform along its edge at the speed of 1.09 m/s with respect to the platform. Your 20.9-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 17.5-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 1.95 m. Calculate the total angular momentum of the system.
Explanation / Answer
Given
Circular platform rotates ccw 90.5kg, radius 1.95 m, 0.877 rad/s
You 70.5 kg, cw 1.09 m/s, at r
Poodle 20.9 kg, cw 1.09/2 m/s, at r/2
Mutt 17.5kg, 3r/4
You
Relative
? = v/r
= 1.09/1.95
= 0.5589
Actual
? = 0.877 - 0.5589
= 0.3181
I = mr^2
= 70.5*1.95^2
= 268.07
L = I?
= 268.07*0.3181
= 85.27
Poodle
Relative
? = (1.09/2)/(1.95/2)
= 0.5589
Actual
? = 0.943 - 0.5589
= 0.3841
I = m(r/2)^2
= 20.9*(1.95/2)^2
= 19.86
L = I?
= 19.86*0.3841
= 7.62
Mutt
Actual
? = 0.877
I = m(3r/4)^2
= 17.5(3*1.95/4)^2
= 37.43
L = I?
= 37.43*0.877
= 32.842
Disk
I = mr^2/2
= 90.5(1.95)^2/2
= 172.06
L = I?
= 172.06*0.877
= 150.89
Total
L = 85.27 + 7.62+ 32.84 + 150.89
= 276.97 kg m^2/s
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