Page:Popular Science Monthly Volume 75.djvu/26

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22
THE POPULAR SCIENCE MONTHLY.

a body, and let the arrow T represent a torque acting upon the body. Then the arrow ΔS represents the amount of spin produced by T during a short interval of time, and the diagonal arrow S' represents the actual spin of the body after the torque T has acted for a short interval of time.

(c) The case where the axis of torque is always at right angles to the axis of spin is the most important case, and this case is exemplified in the ordinary gyrostat, which is a wheel and axle supported in a

 

PSM V75 D026 Torque explained 1.png

Fig. 5. Fig. 6.
 

movable frame as shown in Fig. 7. By taking hold of the frame it is impossible to exert a torque upon the wheel except about an axis perpendicular to OS, friction at pivots being ignored. If the frame be suspended by a string as shown in Fig. 7 (side view), the pull of the earth combined with the pull of the string constitutes a torque as indicated by the arrow T in Fig. 7 (top view). The effect of this torque during a short interval of time is to produce a certain amount of spin, or spin-momentum, ΔS about T as an axis, and the resultant axis of spin

 

PSM V75 D026 Torque explained 2.png

Fig. 7.

 

becomes S' as shown in the diagram Fig. 7. The unbalanced torque T, due to the weight of the wheel and frame in Fig. 7, causes the frame and wheel to sweep round and round in a horizontal plane about the supporting string as' an axis. This kind of motion of an axis of spin due to a torque which is at each instant at right angles to the axis of spin is called precession, and the axis PP, Fig. 7, about which the axis of spin rotates is called the axis of precession.