Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1905 Excerpt: ...symmetry. About what axis will the cylinder begin to turn? The forces have a moment about the longitudinal axis, and also about a transverse one through the centre of mass. If the angular acceleration about each of the axes were the same, it can be shown that the resultant rotation would be about an axis perpendicular to the plane containing the couple; for the relation between the component accelerations would be the same as between the component moments producing them. But this is not the case. The body is more easily set in rotation about one axis than about another; thus, about the longitudinal axis, motion is produced more easily owing to the small moment of inertia with respect to this axis; on the other hand, motion about the transverse axis is generated only with difficulty. The consequence is that the resultant motion more nearly consists in a rotation round the longitudinal axis than might at first be expected. It can be shown that there are always three principal axes, the rotation produced about each of which can be found by the rules given in this chapter; the actual motion consists in the superposition of these three motions. This complication is excluded from the cases dealt with in this chapter, in all of which the forces have a moment about one principal axis only--viz. that which is perpendicular to the plane of symmetry. Illustrative Examples. 1. A reel is allowed to fall, the thread being attached to a fixed support. Supposing the thread keeps tight and vertical throughout, calculate the acceleration of the centre of mass of the reel Fig. 98. (Fig. 98). We shall suppose the reel to be fully wound, and further that the amount of thread removed during the fall is so small that the mass of the reel remains sensibly constant. The external fo...
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