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Chapter 14 - ROTATIONAL DYNAMICS FOR RIGID BODIES

Published online by Cambridge University Press:  05 August 2013

Steven C. Frautschi ,
Richard P. Olenick ,
Tom M. Apostol  and
David L. Goodstein
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Summary

If each element of a body be multiplied into the square of its distance from the axis 0A and all these products be collected into one sum and if this is put = Mkk, which I call the moment of inertia of the body with respect to the axis 0A, then the moment of force required to produce acceleration α will be Mkk · α.

Leonhard Euler, in Theoria Motus Corporum Solidorum seu Rigidorum (1765)

ROTATION OF A RIGID BODY ABOUT A FIXED AXIS

The motion of bodies is determined by Newton's laws. The detailed application of these laws, however, to actual problems such as the motion of the earth under all forces exerted on it by the sun, the moon, and the other planets is a complex matter. One of the main difficulties is that the earth does not spin about a fixed axis in space. Another complication, which manifests itself in tides, is that the earth is not perfectly rigid.

We will tackle some of these complications in due course, but for the present we confine our attention to rigid bodies rotating about fixed axes. The rotation of a flywheel, for example, occurs about a fixed axis. The rolling of a wheel along a straight path involves rotation about an axis which, while moving in space, does not change its direction.

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The Mechanical Universe
Mechanics and Heat, Advanced Edition
 , pp. 363 - 412
Publisher: Cambridge University Press
Print publication year: 1986

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