THE CENTRIPETAL-CENTRIFUGAL FORCE
Bert Schreiber
4519 Holly St.
Bellaire, TX 77401-5802
[email protected]
Abstract: The present concept of the centripetal force, centripetal acceleration, and the centrifugal force results in
that they are imaginary. Yet, a centrifuge operates and exists. Therefore, there is no explanation or theory, much
less any equations that can explain why sparks fly off a rotating body, say a grindstone, at a tangent. The
problems that these created were the meaning of words in the English language. This paper only gives the present
mechanical solution. The spark problem cannot be addressed here as its solution requires the usage of the author’s
new theory.
1. OPENING:
Current theories use the geomathematics of point, lines, and pi and so must be used here. The English
dictionaries for generic and scientific words when correct then define the words used herein.
Centrifugal: outwards. Centripetal: inwards. The result is: The centripetal and centrifugal force is
imaginary.
This is because any force has an equal and opposite force. In accordance with the mathematical rules for
vectors, such equal and opposite vectors result in a zero effect. The net force between any source of
force is then zero. i.e., ←0→. That means the centripetal acceleration is like wise imaginary. Simply, a
point on the rotating circle cannot go one point out on a tangent and then move down one point or back
to its origin on the circle. In reality, an atom cannot jump out from the rim some length, its own
diameter, and then jump back in the same length. Because, if all of the atoms did so, said atom at that
new radius would then jump etc. and the rotating mass would disintegrate or explode. The scientist’s
beliefs override simple facts or logic.
At the sake of overkill, consider two equal masses affixed to a common fisherman’s spring scale, one to
the hanger on its case at its top and one to the free moving hook on its bottom. Now rotate this
combination and the spring scale will have a reading showing the total centrifugal force “effect”, 1/2
from each mass. This is a perfect example of a “controlled experiment”. From the author’s first year
college physics textbook AN INTRODUCTORY COURSE IN COLLEGE PHYSICS, Newton Henry
Black, The Macmillian Company1935, there is shown a centrifugal force piece of apparatus that has
such a weighted spring and scale built into it. Likewise, all the equations used W or weight. Modern
textbooks use “mass”(m) that is absurd and FALSE. A copy of this page follows. Read it carefully. This
illustration has long been removed from all current textbooks.
Note that in the text Black has a mistake – force depends on three factors, BUT, in the equation is a
fourth one or g (gee). But also note, he has labeled correctly the body as Mass but uses weight in the
equation.
In order to prove the existence of that centrifugal force, the experimenter chose a specific instrument that
is illegal. Such scales operate by two mechanical configurations.
The first is using an expansion spring fixed to the top of the case. Attached to the lower end of the spring
is the top of the hook with a hand (pointer) at right angles to read off the force on a division scale on the
side of the case. Both the spring and the hook are only effective to the hanger (on the case). The second
kind is using a compression spring with the top of the hook with its hand on the top of the spring, but,
the bottom of the spring is fixed to the case, so both are again, only effective at/to the hanger.
The legitimate instrument is different. Replace that spring scale with an expansion spring with a pointer
attached to the spring sticking up at the common center of rotation with the weights attached to the ends
of the spring and rotate again. The pointer does not move as the force at the exact point center is zero as
the two equal and opposite centrifugal “forces” effect likewise, cancel.
What is not in textbooks today is this zero effect. Using a compression spring and pushing on the ends
results in that zero force again at the center. Likewise, pressing ones thumb tip against the index finger
tip results in zero force between them. The force effect is not at the exact center plane as that is zero, but
must START at some length away from the center and flattens out the muscles. What is that length is
not for here, just remember this FACT.
Why is all of this including mass and weight as noted? Because, this piece of apparatus will give
different values for the answer for the amount of measured force when it is used elsewhere.
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Specifically in order; on the Earth and where it is, i.e., equator or at the poles etc., on the Moon, and
aboard the space shuttle under micro-gravity conditions, i.e., near weightless. That Mass’s weight
changes with each location due to the change in gee and the smaller the weight, the less the force! It has
its minimum force when in near weightless conditions. Unfortunately the implications of this cannot be
given here. Why current usage of m(ass) is absurd is now apparent and why it is false. Doesn’t in reality
even give the correct answer with m or W anywhere on the Earth as any weight constantly changes,
i.e., gee.
2. SOURCE OF THE FORCE:
For brevity, C and C will mean the centripetal and centrifugal force. The C and C currently exist and are
part and parcel of Newton’s three Laws of Force and Motion. The Third Law covers the equal and
opposite forces.
FIGURE 1
The above figure explains why there is a real centrifugal force but NOT a centripetal force per se. To
understand this, requires a brief return to the definition of the word work. Work is moving some mass
some length that is PATH INDEPENDENT from point a to point b AGAINST the force that requires the
expenditure of energy. The time, technically required to do so is not material. It would matter not
whether it took a year or a billion years, the amount of energy expended is almost identical. But, that is
not the correct statement. The time involved does have a bearing as to the amount of ENERGY required
in the elapsed time involved. That is because F = ma (1) or it is that acceleration that changes the
mv2
(2). Therefore to
quantity of work required to impart the kinetic energy stored in said mass. KE =
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double the acceleration, hence the elapsed time required, takes twice as much input energy.
In order to fully understand the C and C requires the usage of four scenarios. No drawing of same as
they are easily visualized and the readers may have already witnessed one them in action.
3. SCENARIO 1:
This is just a rotating wheel whether it is in free space or here on Earth. A normal grinding wheel with
its attached electric motor with a speed control affixed to the work stand or bench will be used, but
remember it could be just that wheel out in space.
In FIGURE 1, the symbol h in place of r for radius or L for length was used as to its implied connation.
Simply, some mass is to be raised some height in some unit of time, hence undergoes an acceleration.
Now pay attention!
When the wheel is not rotating, there is no additional force on the atoms of the wheel, hence no C and C.
Now turn on the motor and start the wheel rotating very slowly, say one revolution per minute.
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It has now changed from Newton’s First Law to the Second Law. Taking point a as an atom of mass on
the surface of said wheel, it then starts to move along the arc of said circle from point a to point b at the
top. But, its path is independent as the actual height moved is NOT the length of the arc but simply that
from o (center of wheel) or vertical from a to top line, to point b or its h. It would take15 seconds of
elapsed time to do so.
It therefore has accelerated from maximum starting at point a to zero when it reaches point b as it is no
longer or cannot go any higher or the h is now the maximum height attained. It has now stored some
kinetic energy and has obeyed Newton’s Second Law. And that is where the EFFECT of centrifugal
force comes into existence. The atom has moved or has been pushed outwards from a to b and is the
same, not identical, as if it had moved from point o to point b or ”impacted” at point b and so is pushed
or actually IS pushing outwards creating the effect. This gets complicated. It is still pushing when at
point a or has a force, but once it has gone maximum h, the acceleration push out effect no longer exists.
Then in accordance with Newton’s Third Law there must be some opposite force. That is the atom at
point c moving to point d in the opposite direction exerting the centrifugal force effect at point d. So,
where is the so called centripetal force? That is actually the centrifugal force that is 180 degrees out of
phase to the first centrifugal force or gives the imaginary effect of a force from a to o to counteract the a
to b force, whereas it is actually the force from o to d. So, the centripetal force is imaginary or the actual
opposite centrifugal force has been renamed centripetal force or is double-named. Last line of third
paragraph from the bottom on page 2.
When a and c are the two atoms or any two opposing, then there is that as was shown at the start of this
paper. a ←0→ c.
Now it is easily explained and seen that as the rotational speed increases, that more and more energy
and the increased resulting force is required to move the atom from a to b in a shorter elapsed time.
It is also obvious that the larger the mass, that the larger the force. Hence a centrifuge simply separates
lighter from heavier masses; the heavier they are the faster they get spun outwards to stick to the inside
of whatever stops them. And who sees what due to frames of reference will be ignored. Not for here.
4. SCENARIO 2:
This will use the first scenario, but the motor will be battery powered. Here can be done an actual
experiment. Assume again for simplicity, that the wheel and the motor-battery have the same mass
distribution or their masses are equal. Then holding the motor in your hand turn it on. Now toss it up in
the air. The motor will start to spin in the opposite direction to the wheel until both are rotating the same
or at on-half the wheel’s original rotational speed. There is no gyroscopic effect or said effect is
cancelled out. The motor-wheel will simply act as a non rotating mass and follow the path as provided
for under current theories after its release; minutiae skipped.
5. SCENARIO 3:
For this scenario the wheel is not balanced. For brevity, say some of its mass has been removed or a hole
made near its rim and is still affixed to the stand or workbench. Then turn it on at a low speed.
When it is going one revolution per minute, it will show no visible effect. In fact, it would be very hard
to detect. BUT, turn up the speed control and soon the motor-wheel will start to vibrate. If the speed was
further increased, eventually the wheel would vibrate or shatter with dire results.
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Again, follow the first scenario and the opposite centrifugal force is now unbalanced and is transmitted
to the stand or workbench. Something has to give.
There are many devices that use this effect; body massagers, concrete vibrators to get rid of air bubbles,
road tampers and such other devices. Did any reader accidentally using an electric drill bend the drill
bit? How about hitting your rotating grass mower blade on a rock or something and bending the motor
shaft?
6. SCENARIO 4:
We will go back to the wheel-battery motor. Make the wheel unbalanced. Even better, replace it with a
short vertical bar with one end is affixed to the shaft. Now turn it on and set it on the floor. It will vibrate
and bounce all around in divers, like a chicken with its head cut off, directions something terrible. Now
toss it up and see what happens. No more vibrations as its path through the air will be normal. No more
vibrations as the two centrifugal forces cancel one another automatically as those two masses are now
rotating about their common center of gravity or mass.
7. FUNDAMENTAL PROOF:
8. CONCLUSIONS:
1. The centrifugal force and its effect exist.
2. The centripetal force does not exist per se.
3. The centrifugal force each has its own equal and opposite centrifugal force.
4. There is no centripetal acceleration under the current geomathematical theory.
5. Why sparks fly off etc. cannot be explained under current theory.
When a specific centrifuge, all factors remain the same, is used on the Earth, let it be assumed it had to
operate for one hour to perform its intended separation function for the involved mass/weight. Then it is
taken to the Moon and it will take far longer, about 6 times to be more exact, to perform the identical
function as if it was on the Earth. Then if it was placed aboard the space shuttle in orbit, it would still
take far longer to perform its function.
The author will leave it to the reader to determine, relative that is, the exact time ratios required, i.e., one
unit time, pick your starting point, on the shuttle, on the Moon, and on the surface of the Earth.
EPILOG:
But there is a big problem. Once any atom has moved from one point on the rim to another point 90
degrees away, it no longer is moving outwards and so it is no longer accelerating.
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And if it is NOT accelerating, it is not moving or has stopped. Then at that point it is accelerating
towards the next point 90 degrees away. Paradox! It cannot be both stopped and accelerating at the same
instant of time.
For simplicity, the center of the shaft has a small hole along its axis. This then holds true for any atom
comprising said wheel and shaft. Therefore, the wheel is rotating or moving and not one single other
atom is moving or has STOPPED. And IF all of them are stopped, then the wheel is NOT MOVING.
No problem. Figure it out for yourselves. Hint; semantics! Or is it frames of reference?
February 2007
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