Page:Popular Science Monthly Volume 75.djvu/25

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21
GYROSTATIC ACTION

of the body will be represented in magnitude and in direction by the arrow R.[1] That is to say, after the large turning force has acted for a short time the body will be found spinning about R as an axis, and the number of revolutions per second will be represented by the length of R. The geometrical relationship between the arrows S', S", and R is completely represented in the triangle OMN of Fig. 2, which triangle is shown by itself in Fig. 3.

A turning force is usually called a torque, thus the turning or

 

PSM V75 D025 Geometric relationship of torque to spin.png

Fig. 2. Fig. 3.
 

twisting force which is exerted upon a screw driver is a torque. A torque may be completely represented by an arrow drawn parallel to the axis of the torque, pointing in the direction in which a right-handed screw would travel if turned by the torque, and having a length which represents the magnitude or value Fl of the torque to scale. Thus the arrow T in Fig. 4 represents the torque due to the two forces FF.

The effect of an unbalanced torque upon a body is to produce a spin-velocity about the same axis as the torque, the amount produced

 

PSM V75 D025 Representation of the torque force on spin.png

Fig. 4.

 

being proportional to the time the torque continues to act and inversely proportional to what is called the moment of inertia of the body, (a) The simplest case is where the axis of the torque is parallel to the axis of already existing spin as shown in Fig. 5, which represents a wheel and axle set spinning by pulling a cord which is wound around the axle. In this case the axle of spin remains stationary, and the magnitude of the spin increases steadily as long as the torque continues to act. (b) The general case is where the axis of the torque makes any angle whatever with the axis of the already existing spin. Thus, let the arrow S, Fig. 6, represent the already existing spin of

  1. This proposition is entirely correct if by spin we understand that spin momentum is meant; the spin-velocity of a body is sometimes greatly complicated by its lack of symmetry, and these complications are ignored in the present discussion.