Hoop System
Jan/110
Find the angular momentum of the system!!!!?
Two gerbils run in place with a linear speed of 0.48 m/s on an exercise wheel that is shaped like a hoop. Find the angular momentum of the system if each gerbil has a mass of 0.24 kg and the exercise wheel has a radius of 9.1 cm and a mass of 3.7 g.
If the gerbils are "running in place" that means they have no velocity with respect to the center of the wheel, so they contribute no angular momentum. However, if they run in place, the wheel must move under them at the same velocity, so the tangential velocity of the wheel is 0.48 m/s. The angular velocity ω = v/r = 0.48/r. The angular momentum of the wheel is I*ω, where I = moment of inertial. If the wheel's mass is all at the rim, I = m*r²
p = (0.48/r)*m*r² = 0.48*m*r
p = 0.48*0.0037*0.091 = 1.6*10^-4 kg-m²/s
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