Substituting in the formula and solving:5R— = —¼10This means that the screwdriver blade will turnthe screw with a force of 200 pounds. The relationshipbetween the radius of the diameters or thecircumferences of the wheel and axle tells you howmuch mechanical advantage you can get.Take another situation. You raise the old oakenbucket, figure 3-2, using a wheel-and-axle arrangement.If the distance from the center of the axle to the handleis 8 inches and the radius of the drum around which therope is wound is 2 inches, then you have a theoreticalmechanical advantage of 4. That’s why these rigs wereused.MOMENT OF FORCEIn several situations you can use the wheel-and-axleto speed up motion. The rear-wheel sprocket of a bike,along with the rear wheel itself, is an example. Whenyou are pedaling, the sprocket is attached to the wheel;so the combination is a true wheel-and-axle machine.Assume that the sprocket has a circumference of 8inches, and the wheel circumference is 80 inches. If youturn the sprocket at a rate of one revolution per second,each sprocket tooth moves at a speed of 8 inches persecond. Since the wheel makes one revolution for eachrevolution made by the sprocket, any point on the tiremust move through a distance of 80 inches in 1 second.So, for every 8-inch movement of a point on thesprocket, you have moved a corresponding point on thewheel through 80 inches.Since a complete revolution of the sprocket andwheel requires only 1 second, the speed of a point on thecircumference of the wheel is 80 inches per second, or10 times the speed of a tooth on the sprocket.(NOTE: Both sprocket and wheel make the samenumber of revolutions per second, so the speed ofturning for the two is the same.)Here is an idea that you will find useful in under-standing the wheel and axle, as well as other machines.You probably have noticed that the force you apply to alever starts to turn or rotate it about the fulcrum. Youalso know that a sheave on a fall starts to rotate thesheave of the block. Also when you turn the steeringwheel of a car, it starts to rotate the steering column.Whenever you use a lever, or a wheel and axle, youreffort on the lever arm or the rim of the wheel causes itto rotate about the fulcrum or the axle in one directionor another. If the rotation occurs in the same directionas the hands of a clock, we call that direction clockwise.If the rotation occurs in the opposite direction from thatof the hands of a clock, we call that direction of rotationcounterclockwise. A glance at figure 3-3 will make clearthe meaning of these terms.The force acting on the handle of a carpenter’s bracedepends not only on the amount of that force, but alsoon the distance from the handle to the center of rotation.This is known as a moment of force, or a torque(pronounced tork). Moment of force and torque have thesame meaning.Look at the effect of the counterclockwisemovement of the capstan bar in figure 3-4. Here theamount of the effort is designated El and the distancefrom the point where you apply the force to the centerFigure 3-2.-The old oaken bucket.Figure 3-3.-Directions of rotation.3-2

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