Substituting in the formula and solving:
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. Thats why these rigs were
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 carpenters 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
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.