Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/399

Rh dealing with the gyroscope which has many points in its favour. The account that follows forms a portion of a paper read before the Institution of Automobile Engineers.

"The fundamental principle employed in the following exposition is termed the principle of the conservation of angular momentum. This is the rotational analogue of the conservation of (linear) momentum, which is corollary to the third law of motion—When force acts on a body, the momentum generated in unit time is proportional to the force. The rotational form of this law is—When a couple or 'torque' acts on a body about a given axis the angular momentum generated per unit time about that axis is proportional to the magnitude of the torque.

"In both cases the term 'body* may be construed as including not only a rigid body, or body in one piece, but a complex body of any kind whatever consisting of an indefinite number of parts associated amongst themselves by any known or unknown laws of attraction or repulsion. In other words, for body we may substitute the term self-contained system—such a system being one not associated with its surroundings in any way whatever except as regards the specified applied force, or torque, as the case may be.

"As it is important that the signification of the above principles should be made quite clear, an illustration will not be out of place. A well-known application of the principle of the conservation of momentum is the case of the gun and projectile: when a gun is mounted so that it is quite free to recoil, in fact, so that we may regard it as constituting with its charge and projectile a self-contained system, the firing of the charge has no influence on the motion of the mass centre of the system, so that when the shot and powder gases are projected forward the gun recoils backward, the minus momentum of the gun exactly neutralising the plus momentum of the charge. In order to reduce this problem to a nice simple form, it is usual to suppose that the {[c|375}}