Substituting  in  the  formula  and  solving: 5 R —   =   — ¼ 10 This means that the screwdriver blade will turn the screw with a force of 200 pounds. The relationship between   the   radius   of   the   diameters   or   the circumferences of the wheel and axle tells you how much mechanical advantage you can get. Take another situation. You raise the old oaken bucket, figure 3-2, using a wheel-and-axle arrangement. If the distance from the center of the axle to the handle is 8 inches and the radius of the drum around which the rope is wound is 2 inches, then you have a theoretical mechanical advantage of 4. That’s why these rigs were used. MOMENT  OF  FORCE In several situations you can use the wheel-and-axle to speed up motion. The rear-wheel sprocket of a bike, along with the rear wheel itself, is an example. When you 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 8 inches, and the wheel circumference is 80 inches. If you turn the sprocket at a rate of one revolution per second, each sprocket tooth moves at a speed of 8 inches per second. Since the wheel makes one revolution for each revolution made by the sprocket, any point on the tire must move through a distance of 80 inches in 1 second. So,  for  every  8-inch  movement  of  a  point  on  the sprocket, you have moved a corresponding point on the wheel  through  80  inches. Since a complete revolution of the sprocket and wheel requires only 1 second, the speed of a point on the circumference of the wheel is 80 inches per second, or 10 times the speed of a tooth on the sprocket. (NOTE: Both  sprocket  and  wheel  make  the  same number  of  revolutions  per  second,  so  the  speed  of turning 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 a lever starts to turn or rotate it about the fulcrum. You also know that a sheave on a fall starts to rotate the sheave of the block. Also when you turn the steering wheel of a car, it starts to rotate the steering column. Whenever you use a lever, or a wheel and axle, your effort on the lever arm or the rim of the wheel causes it to rotate about the fulcrum or the axle in one direction or another. If the rotation occurs in the same direction as the hands of a clock, we call that direction clockwise. If the rotation occurs in the opposite direction from that of the hands of a clock, we call that direction of rotation counterclockwise. A glance at figure 3-3 will make clear the meaning of these terms. The force acting on the handle of a carpenter’s brace depends not only on the amount of that force, but also on 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 the same  meaning. Look   at   the   effect   of   the   counterclockwise movement of the capstan bar in figure 3-4. Here the amount of the effort is designated  El and the distance from the point where you apply the force to the center Figure 3-2.-The old oaken bucket. Figure 3-3.-Directions of rotation. 3-2