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) $1020 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
B) $975 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
C) $940 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
D) $1500 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$

Question

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) $1020 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
B) $975 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
C) $940 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
D) $1500 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$

Quizplus · Accepted Answer

The angular momentum $L$ of a solid, uniform cylindrical flywheel is given by $L = I\omega$, where $I$ is the moment of inertia of the cylinder ($I = \frac{1}{2}MR^2$ for a solid cylinder) and $\omega$ is the angular velocity. For each flywheel, $I = \frac{1}{2} \times 65.0 \, \text{kg} \times (1.47 \, \text{m})^2$. The net angular momentum is the sum of the angular momenta of the three flywheels, taking into account the direction of rotation. Two flywheels rotate in one direction and one in the opposite, so their angular momenta subtract. Calculating the net angular momentum gives approximately $1020 \, \text{kg} \cdot \text{m}^2/\text{s}$.

Three Solid, Uniform, Cylindrical Flywheels, Each of Mass 65 1020 kg⋅m2/s1020 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }1020 kg⋅m2/s

Three Solid, Uniform, Cylindrical Flywheels, Each of Mass 65 $1020 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$