Three solid,uniform 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.

Question

Quizplus · Accepted Answer

The net angular momentum is the sum of the angular momenta of the individual flywheels. The angular momentum of a flywheel is given by L = Iω, where I is the moment of inertia and ω is the angular velocity. The moment of inertia of a solid, uniform flywheel is given by I = (1/2)MR^2, where M is the mass and R is the radius.For the two flywheels rotating in the same direction, the angular momenta are:L1 = (1/2)(65.0 kg)(1.47 m)^2(3.83 rad/s) = 257 kg∙ m^2/sL2 = (1/2)(65.0 kg)(1.47 m)^2(3.83 rad/s) = 257 kg∙ m^2/sFor the flywheel rotating in the opposite direction, the angular momentum is:L3 = (1/2)(65.0 kg)(1.47 m)^2(-3.42 rad/s) = -222 kg∙ m^2/sThe net angular momentum is:Lnet = L1 + L2 + L3 = 257 kg∙ m^2/s + 257 kg∙ m^2/s - 222 kg∙ m^2/s = 298 kg∙ m^2/s

Three Solid,uniform Flywheels,each of Mass 65