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. 1917 edition. Excerpt: ...an axis through this centre. From their mutuality the two translational forces are equal and opposite and the two couples are equal and opposite, or their axes are in opposite directions, since a couple is represented by a vector. The force in any direction is the rate at which the potential energy is used up ...
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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. 1917 edition. Excerpt: ...an axis through this centre. From their mutuality the two translational forces are equal and opposite and the two couples are equal and opposite, or their axes are in opposite directions, since a couple is represented by a vector. The force in any direction is the rate at which the potential energy is used up in that direction, or the derivative of the potential with respect to the direction. The force urging dV the centres of inertia together is-r= If we simply turn the aK bodies about R, the potential is not altered. Considering the second body simply as a material point of mass M', Equa. (1) becomes V_ml + M-f(?). (2) It will be noted that the attraction in the plane of the equator of a spheroid is greater than if the mass were concentrated into its centre, while the attraction in its axis is less, or for equal distances the attraction is a maximum in the plane of the equator and a minimum in the axis. It will also be noted that the motion of the centre of inertia is the same whether we apply the forces parallel to their original directions to this centre, or subject the mass concentrated into this centre to the field. In general this is not the case. See Art. 8. If 7 is the angle which R makes with the equator of the spheroid, then the couple tending to bring the equatorial dV 3M' dl plane into coincidence with R is (C--A) sin 7 cos 7, since I K3 to a close approximation. 25. Rotary Motion A disc spins (Fig. 11) on its axis PP', which is held in a ring which can turn about a horizontal axis HH', and the whole turns about a vertical axis VV. If the disc is not rotating and we turn it about the vertical axis, it will simply obey the turn and its axis PP' will remain in the horizontal plane. If it is rotating and we turn the axis through a...
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