=121. The Lever.=--The _lever_ is one of the simple machines most frequently used, being seen in scissors, broom, coal shovel, whip, wheelbarrow, tongs, etc. _The lever consists of a rigid bar capable of turning about a fixed axis called the fulcrum._ In studying a lever, one wishes to know what weight or resistance it can overcome when a certain force is applied to it. Diagrams of levers, therefore, contain the letters _w_ and _f_. In addition to these, _O_ stands for the fulcrum on which it turns. By referring to Fig. 86, _a_, _b_, _c_, one may notice that each of these may occupy the middle position between the other two. The two forces (other than the one exerted by the fulcrum) acting on a lever always oppose each other in the matter of changing rotation. They may be considered as a pair of parallel forces acting on a body, each tending to produce rotation. [Illustration: FIG. 86.--The three classes of levers.] =122. Moment of Force.=--The _effectiveness_ of each force may therefore be determined by computing its _moment_ about the fixed axis (see Art. 84), that is, by multiplying each force by its distance to the fulcrum or axis of rotation. Let a meter stick have a small hole bored through it at the 50 cm. mark near one edge, and let it be mounted on a nail driven into a vertical support and balanced by sliding a bent wire along it. Suspend by a fine wire or thread a 100 g. weight, 15 cm. from the nail and a 50 g. weight 30 cm. from the nail, on the other side of the support. These two weights will be found to balance. When viewed from this side _A_ (Fig. 87) tends to turn the lever in a clockwise direction (down at right), _B_ in the counter-clockwise direction (down at left). Since the lever balances, the forces have equal and opposite effects in changing its rotation as may also be computed by determining the moment of each force by multiplying each by its distance from the fulcrum. Therefore the _effectiveness_ of a force in changing rotation depends upon the distance from it to the axis as well as upon the magnitude of the force. [Illustration: FIG. 87.--The two moments are equal about _C_. 100 × 15 = 50 × 30.] From the experiment just described, the moment of the acting force equals the moment of the weight or _f × D_{f} = w × D_{w}_, or the effort times the effort arm equals the weight times the weight arm. This equation is called the law of the lever. It corresponds to the general law of machines and may also be written _w: f = D_{f}: D_{w}_.