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

Physics

Pitts

2 March, 15:29

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.

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Snow White · Answer 1

297.77 kg m^2 / s

Explanation:

mass of each flywheel, m = 65 kg

radius of flywheel, r = 1.47 m

ω1 = 3.83 rad/s

ω2 = - 3.42 rad/s

Moment of inertia, I = 1/2 mr² = 0.5 x 65 x 1.47 x 1.47 = 70.23 kg m^2

Angular momentum is defined as

L = I x ω

Net angular momentum

L = 2 x I x ω1 - I x ω2

L = 2 x 70.23 x 3.83 - 70.23 x 3.42

L = 537.96 - 240.19

L = 297.77 kg m^2 / s

Thus, the angular momentum is 297.77 kg m^2 / s.