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Moments of Inertia of Disks and Spheres Without Integration
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1.
1.D. E. Rutherford, “How to find moments of inertia without actually integrating,” Math. Gaz. 44, 59 (Feb. 1960).
http://dx.doi.org/10.2307/3608512
2.
2.B. Oostra, “Moment of inertia without integrals,” Phys. Teach. 44, 283285 (May 2006).
http://dx.doi.org/10.1119/1.2195398
3.
3.W. L. Anderson, “Noncalculus treatment of steady-state rolling of a thin disk on a horizontal surfacePhys. Teach. 45, 430433 (Oct. 2007).
http://dx.doi.org/10.1119/1.2783152
4.
4.D. C. Giancoli, Physics for Scientists and Engineers, 4th ed. (Addison-Wesley, New York, 2008), p. 265.
5.
5.See, for example, C. E. Swartz and T. Miner, Teaching Introductory Physics (AIP Press, New York, 1997), pp. 174,176.
http://aip.metastore.ingenta.com/content/aapt/journal/tpt/51/3/10.1119/1.4792004
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Fig. 1.

Disk of radius R and mass M is made up of a large number N (→ ∞) of infinitesimally thin rods. The ith rod having length and mass is shown. Its center is a distance from the center of the disk.

Image of Fig. 2.

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Fig. 2.

Sphere of radius R and mass M is made up of a large number N (→ ∞) of infinitesimally thin disks. The ith disk having radius and mass is shown. Its center is a distance from the center of the sphere.

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/content/aapt/journal/tpt/51/3/10.1119/1.4792004
2013-02-08
2014-04-19

Abstract

Calculation of moments of inertia is often challenging for introductory-level physics students due to the use of integration, especially in non-Cartesian coordinates. Methods that do not employ calculus have been described for finding the rotational inertia of thin rods and other simple bodies.1–3 In this paper we use the parallel axis theorem and the perpendicular axis theorem (both of which may be proved without calculus 4), along with rotational symmetry, to determine, without using integration, the moments of inertia of uniform disks and spheres.

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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Moments of Inertia of Disks and Spheres Without Integration
http://aip.metastore.ingenta.com/content/aapt/journal/tpt/51/3/10.1119/1.4792004
10.1119/1.4792004
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