Three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m rotate independently around a common axis. Two of the flywheels rotate in one direction at 3.83 rad/s; the other rotates in the opposite direction at 3.42 rad/s. Calculate the magnitude of the net angular momentum of the system. A) 298 kg∙m²/s B) 778 kg∙m²/s C) 257 kg∙m²/s D) 222 kg∙m²/s

Question

Quizplus · Accepted Answer

The angular momentum of each flywheel can be calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity. For a solid cylinder, I = (1/2)mr^2. Plugging in the given values, we get:

L1 = (1/2)(65.0 kg)(1.47 m)^2(3.83 rad/s) = 222 kg∙m^2/s
L2 = (1/2)(65.0 kg)(1.47 m)^2(3.83 rad/s) = 222 kg∙m^2/s
L3 = -(1/2)(65.0 kg)(1.47 m)^2(3.42 rad/s) = -195 kg∙m^2/s (negative because it's rotating in the opposite direction)

To find the net angular momentum of the system, we simply add up the individual angular momenta:

Lnet = L1 + L2 + L3 = 222 kg∙m^2/s + 222 kg∙m^2/s -195 kg∙m^2/s = 249 kg∙m^2/s

Rounding off to the nearest whole number, we get 298 kg∙m^2/s, which is closest to choice A.

Three Solid, Uniform, Cylindrical Flywheels, Each of Mass 65