Since the moment of the power must equal the moment of the weight whenever there is equilibrium, we have, from Fig. 1, PR=Wr ; or, in the form of a proportion,
P: W = r: R. …….(1)
FIG.1.
This can be stated as follows: A certain power applied to the wheel and axle can support a weight as many times greater than itself as the radius of the wheel is times greater than the radius of the axle. The radii in Formula 1 can be replaced by either the circumferences or the diameters if it is more convenient.
The mechanical advantage of the wheel and axle is the ratio of R to r. If the power and weight are disposed as in Fig. 1, the mechanical advantage is one of force; if the points of application of P and W are interchanged, it is one of speed.
The wheel and axle is used to raise water from a well, to hoist ore from a mine, as with the windlass, to move buildings, and to raise anchors, as with the capstan. In the capstan no wheel is used, but instead straight bars, called hand-spikes, are put into holes in the head of the capstan, and the power is applied to these.
