A horizontal circular platform rotates counterclockwise about its axis at the ra
ID: 1520421 • Letter: A
Question
A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.951 rad/s. You, with a mass of 73.1 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 19.1-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 91.1 kg and radius 1.89 m. Calculate the total angular momentum of the system.
Explanation / Answer
for the platform :
M = mass of platform = 91.1 kg
R = radius = 1.89 m
I = (0.5)MR2 = 91.1 (1.89)2 = (0.5) 325.42 kgm2
Wp = angular velocity of platform = 0.0951 rad/s
Lp = angular momentum of plaform = IWp = (0.5) (325.42) (0.951) = 154.74 kgm/s
For the person :
my = mass of person = 73.1 kg
R = radius = 1.89 m
I = my R2 = (73.1 ) (1.89)2 = 261.12 kgm2
Wyp = - 1.09 /R = - 1.09 / 1.89 = - 0.58 rad/s
Wp = 0.951 rad/s
Wyp = Wy - Wp
Wy = Wyp + Wp = - 0.58 + 0.951 = 0.37 rad/s
Ly = Iy Wy = (261.12) ( 0.37) = 96.61
for the pooddle :
mpp = mass of poodle = 21.1 kg
R = radius = 1.89/2 = 0.95 m
Ipp = my R2 = (21.1) (0.95)2 = 19.04 kgm2
Wppp = - 1.09 /2R = - 1.09 / (2 x 1.89) = - 0.29 rad/s
Wp = 0.951 rad/s
Wppp = Wpp - Wp
Wpp = Wppp + Wp = - 0.29 + 0.951 = 0.66 rad/s
Lpp = Ipp Wpp = (19.04) (0.66) = 12.6
For the mutt :
mm = mass of mutt = 19.1 kg
r = distance of mutt = 3R/4 = 3 (1.89)/4 = 1.42 m
Im = moment of inertia of mutt = mm r2 = (19.1) (1.42)2 = 38.5 kgm2
W = 0.951 rad/s
Lm = Im W = 38.5 (0.951) = 36.6
Total angular momentum = L = 154.74 + 96.61 + 12.6 + 36.6 = 300.6
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