Three solid,uniform,cylindrical flywheels,each of mass 65.0 kg and radius 1.47 m,rotate independently around a common axis through their centers.Two of the flywheels rotate in one direction at 8.94 rad/s,but the other one rotates in the opposite direction at 3.42 rad/s.Calculate the magnitude of the net angular momentum of the system. A)1020 kg ∙ m²/s B)1500 kg ∙ m²/s C)975 kg ∙ m²/s D)940 kg ∙ m²/s

Question

Quizplus · Accepted Answer

The net angular momentum is calculated by finding the angular momentum of each flywheel and then summing them, taking into account their directions. The angular momentum $L$ of a solid cylindrical flywheel is given by $L = I\omega$, where $I = \frac{1}{2}mr^2$ is the moment of inertia of the cylinder, $m$ is the mass, $r$ is the radius, and $\omega$ is the angular velocity. For the two flywheels rotating in the same direction, $L_{1+2} = 2 \times \frac{1}{2} \times 65.0 \times (1.47)^2 \times 8.94$. For the one rotating in the opposite direction, $L_{3} = \frac{1}{2} \times 65.0 \times (1.47)^2 \times (-3.42)$. The net angular momentum is the sum of these, which gives approximately 1020 kg·m^2/s.

Three Solid,uniform,cylindrical Flywheels,each of Mass 65