Notes on Mechanics

by Charles R. Cross

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1911 edition. ...An axis about which a body may revolve without causing any tendency to angular deviation is called a principal axis. Any axis about which a body may revolve without producing a tendency to either angular deviation or translation of the axis of rotation is called a free axis. The free axes are evidently principal axes passing through the center of mass. In an ellipsoid with three unequal axes, these are the free axes. In a right elliptical cylinder the free axes are the axis of the cylinder and the major and minor axes of the elliptical middle section of the cylinder. Any diameter of a sphere is a free axis; also, any diameter of the equator of an oblate or prolate spheroid, together with its polar axis. PRACTICAL APPLICATIONS IN Balancing of fly-wheels and other rotating pieces; balancing of crank on driving-wheel of locomotive. 88. Axis of Stable R0tati0Il---An inspection of Fig. 16 will also show that a body is in stable equilibrium only when rotating about its shortest diameter. In machinery several practical considerations frequently require that a rotating piece shall be rotated about a longer rather than a shorter axis of symmetry. This, however, is not a case of free rotation, and the rigidity of the shafting is made such as to counterbalance any centrifugal couple that may be generated. 89. Analogies between Translatory and Rotary Motion.--Some further characteristics of the rotary motion and energy of rigid rotating bodies are most readily considered in this connection. It is easily seen that the effect of a constant unbalanced torque is to produce a uniformly accelerated rotation in a mass, and hence that relations hold between a, w and 0 identical with those which obtain in the case of uniformly accelerated...

30 pages, Paperback

Published September 13, 2013

About the author

Librarian Note: There is more than one author in the Goodreads database with this name.

This is Charles Robert Cross (1848-1921).