A uniform, solid, cylindrical flywheel of radius 1.4 m and mass 15 kg rotates at 2.7 rad/s. What is the magnitude of the flywheel's angular momentum?
A) $40 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
B) $60 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
C) $80 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
D) $20 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$

Question

A uniform, solid, cylindrical flywheel of radius  1.4 m and mass  15 kg rotates at  2.7 rad/s. What is the magnitude of the flywheel's angular momentum?
A) $40 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
B) $60 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
C) $80 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$
D) $20 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$

Quizplus · Accepted Answer

The angular momentum $ L $ of a solid cylinder is given by $ L = I \omega $, where $ I = \frac{1}{2} m r^2 $ is the moment of inertia. Substituting $ m = 15 \, \text{kg} $, $ r = 1.4 \, \text{m} $, and $ \omega = 2.7 \, \text{rad/s} $, we find $ L = \frac{1}{2} \times 15 \times (1.4)^2 \times 2.7 = 39.69 \approx 40 \, \text{kg} \cdot \text{m}^2/\text{s} $.

A Uniform, Solid, Cylindrical Flywheel of Radius 1 40 kg⋅m2/s40 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }40 kg⋅m2/s

A Uniform, Solid, Cylindrical Flywheel of Radius 1 $40 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$