Question

A slender metal rod has a mass $M$ and length $L$. The rod is first rotated about a perpendicular axis through its center with an angular velocity $\omega$ (Figure $9.28 \mathrm{a}$ ). It is then rotated about a perpendicular axis through its end at the same angular velocity (Figure $9.28 \mathrm{~b}$ ). Find the ratio of the kinetic energy of the first case to that of the second case.

Name: A slender metal rod has a mass M and length L. The rod is first rotated about a perpendicular axis through its center with an angular velocity ω (Figure 9.28 a ). It is then rotated about a perpendicular axis through its end at the same angular velocity (Figure 9.28 b ). Find the ratio of the kinetic energy of the first case to that of the second case.
Uploaded: 2024-07-27T19:55:34-08:00
Duration: 2 min 58 s
Channel: Adi S
Description: A slender metal rod has a mass M and length L. The rod is first rotated about a perpendicular axis through its center with an angular velocity ω (Figure 9.28 a ). It is then rotated about a perpendicular axis through its end at the same angular velocity (Figure 9.28 b ). Find the ratio of the kinetic energy of the first case to that of the second case.

          A slender metal rod has a mass $M$ and length $L$. The rod is first rotated about a perpendicular axis through its center with an angular velocity $\omega$ (Figure $9.28 \mathrm{a}$ ). It is then rotated about a perpendicular axis through its end at the same angular velocity (Figure $9.28 \mathrm{~b}$ ). Find the ratio of the kinetic energy of the first case to that of the second case.

Added by Yolanda O.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

07/27/2024

Step 1

First, we need to find the moment of inertia for both cases. For the first case (rotation about the center), the moment of inertia is given by the formula $I_1 = \frac{1}{12}ML^2$. For the second case (rotation about the end), the moment of inertia is given by Show more…

Show all steps

Thanks for your feedback!

A slender metal rod has a mass $M$ and length $L$. The rod is first rotated about a perpendicular axis through its center with an angular velocity $\omega$ (Figure $9.28 \mathrm{a}$ ). It is then rotated about a perpendicular axis through its end at the same angular velocity (Figure $9.28 \mathrm{~b}$ ). Find the ratio of the kinetic energy of the first case to that of the second case.