The moment of inertia of a uniform-density disk rotating about an axle through its center can be shown to be MR. This result is obtained by using integral calculus to add up the contributions of all the atoms in the disk. The factor of 1/2 reflects the fact that some of the atoms are near the center and some are far from the center; the factor of 1/2 is an average of the square distances. A uniform- density disk whose mass is 18 kg and radius is 0.12 m makes one complete rotation every 0.4 s.

The moment of inertia of a uniform-density disk rotating about an axle through its center can be shown to be MR. This result is obtained by using integral calculus to add up the contributions of all the atoms in the disk. The factor of 1/2 reflects the fact that some of the atoms are near the center and some are far from the center; the factor of 1/2 is an average of the square distances. A uniform- density disk whose mass is 18 kg and radius is 0.12 m makes one complete rotation every 0.4 s.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter11: Dynamics Of Rigid Bodies

Section: Chapter Questions

Problem 11.34P

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