Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/400

App. VII. powder gases are without mass, to imagine, in fact, that the projectile is discharged by a repulsive force instead of by gaseous pressure. As so presented the problem is reduced to simple arithmetic: thus, if the projectile weigh 1 oz, and the gun 100 ozs., and if the muzzle velocity of the shot be 2,000 ft./secs., the velocity of recoil is $1⁄100$ × 2,000 = 20ft./secs.

"We may extend the above to deal with the spin of the projectile and the influence of the said spin on the motion of the gun. Thus, when the gun is fired, since there is no torque applied from without, the angular momentum of the self-contained system can undergo no change, and the angular momentum received by the bullet by virtue of the rifling will be exactly neutralised by the opposite angular momentum imparted to the gun. Thus, if the moment of inertia of the gun be 500 times that of the bullet, the angular velocity of the bullet will be 500 times that of the gun, the rotation being, of course, in opposite directions. It may be remarked that the question of the powder gases does not sensibly affect the rotational problem.

"Now in the foregoing illustrations the motions are confined to one line in the case of the linear problem, and about one axis in the analogous case of rotation, but the principles apply equally if the motions involve movements simultaneously along or about the other two co-ordinate axes.

"We will now apply the principle of the conservation of angular momentum to the study of the gyroscope. Taking the case of the ordinary lecture model (Fig. 168), in which the fly-wheel is mounted freely in gimbals, it may at once be noted that the mounting is such as to exercise no kind of rotational restraint on the spinning wheel; the latter is arranged, rotationally speaking, as a self-contained system. Thus, a movement of the stand which forms the mounting, although taking effect translationally on the gyroscope, has no effect rotationally, except so far as may be due to the friction of the gimbals, which is of the nature of a mechanical defect.

"If a torque or couple be applied to the axis of the wheel, or to