The document discusses centripetal and centrifugal forces. It begins by explaining centripetal force as the force acting towards the center in circular motion. It then notes that while centrifugal force is not considered a real force in physics, people experience an outward force in rotating frames. The document proposes that centrifugal force originates from the particle trying to travel in a straight line, which creates tension transmitted to the anchor point and reacted with an equal centripetal force. Thus, centripetal and centrifugal forces exist as equal and opposite reaction forces according to Newton's third law.

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CENTRE SEEKING FORCES

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The Centripetal Force
The particle at P is accelerated
towards the centre because it is
under the influence of a force 𝐹𝐹
acting in the same direction.
According to Newton’s second
law the magnitude of this centre
finding force is:
𝐹𝐹⊥ = 𝑚𝑚𝑚𝑚 = 𝑚𝑚
𝑣𝑣2
𝑟𝑟
Since this force acts along the
direction of the centripetal
acceleration. It is called the
centripetal force.
𝐹𝐹⊥ = 𝑚𝑚𝑚𝑚
𝑣𝑣1
𝑣𝑣2
𝐴𝐴
𝑣𝑣1 = 𝑣𝑣2 = 𝑣𝑣
𝑃𝑃
Centripetal force

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This centripetal force is what we experience in
whirling a weight around. It is also what keeps the
moon in orbit around the earth, and the planets
around the sun, as Newton discovered 300 years ago.
Centripetal forceCentripetal force
Centripetal force
But in the celestial
realm, the force is
provided by gravity
– an action-at-a-
distance (AAAD)
force which is
different from the
contact force in
hurling a ball. We
shall deal with
AAAD in a later
section.
Centripetal force in heaven

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But the story does not end
here. Some kind of force
seems to be missing.

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Any force to balance the
centripetal force?
In conventional mechanics, the
centripetal force is the only force
acting on the particle in circular
motion.
Physicists believe that since the
particle is not in a state of static
equilibrium, there is no need for
the force to be balanced.
But this is obviously in
contradiction to Newton’s third
law which predicts an equal and
opposite force to any force.
𝑣𝑣
P
Missing
force

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Why people experience another force?
People see that mud gets spun off a spinning tire; other see water being pushed out
of the clothes by the spin of the washer; when we go around a curve in our car, there
seems to be some force trying to pull us to the outer side. It seems that there is
another force working outward opposite to the centripetal force. People call it the:
‘Centrifugal Force’.
Centrifugal force Centripetal force

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Ghost of a force
However this centrifugal force
has no place in current physics
as a real force.
Merriam-Webster Dictionary
defines centrifugal force as the
apparent force that is felt by an
object moving in a curved path
that acts outwardly away from
the centre of rotation.
Wikipedia also confirms in
saying that centrifugal force is an
outward force apparent in a
rotating reference frame; it does
not exist when measurements
are made in an inertial frame of
reference.

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Centrifugal force does
not exist
It is believed that the centrifugal
force does not exist in reality.
We only feel it because we are in
a non-inertial coordinate system.
It appears quite real to the
object being rotated because
the object believes that it is in a
non-accelerating situation, when
in fact it is not.

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Centrifugal force does
not exist
Here is an example of the more
emphatic statements:
An evil word has worked its way
into our daily vocabulary, and with
it, an incorrect understanding of
the way physics works.
"Centrifugal Force" . . . . is a
common explanation . . . the only
problem is all of it is absolutely
wrong!!! Centrifugal force does not
exist . . . there is no such a thing . . .
it is a ghost we tend to blame odd
behavior on.
Science by Joy Wagon.
www.regentsprep.org. 2000.
𝑎𝑎

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THE CENTRIFUGAL FORCE
The non-existence of

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New approach
This is a document in Wikipedia
labelled ‘Centrifugal force’,
which promises to have the
reality of centrifugal forces
recovered by the transformation
of frames guided by Einstein’s
theory of relativity. We don’t
quite understand it. But most
probably it describes a force
from the puzzling methods of
mathematical abstraction.
This is not our way of
understanding nature. Instead
we have a simple and straight
forward of identifying this
mysterious centrifugal force
presented as follows.
Transform!!!!
# & @ * % $

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The incompatibility gap
The new force comes up mainly
due to the geometry of the
straight line and the circle.
If we examine the circular
motion diagram more closely, we
can see that the straight line,
although tangent to the circle at
a point, never shows any sign of
compatibility with the circle.
Besides the contact point, there
is always a widening gap
between them.
𝑣𝑣
The ever existing
incompatibility gap

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The existence of the
Centrifugal Force
The existence of this gap
indicates that the particle is
always in the motion of leaving
the circle.
This does not mean that the
particle is flying away from the
circle, it is only trying to travel
straight forward. In doing so, it is
inevitable that it is getting away
from the curve of the circle.
This getting away constitutes a
pulling force in the string trying
to get it longer. This is the origin
of the centrifugal force.
𝑟𝑟
𝑣𝑣
𝐴𝐴
𝑃𝑃
𝑄𝑄
Pull
Pull
𝑣𝑣
Trying to leave
the circle

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The pull travels to the centre
This pulling by the particle sets
the string in tension which
transmits the pulling force down
to the anchor point A.
𝑟𝑟
𝑣𝑣
𝐴𝐴
𝑃𝑃
𝑄𝑄
Stress
travels
down to A
Pull
Pull

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The existence of the Centrifugal
Force
The anchor point counteracts
instantly with a pull.
𝑟𝑟
𝑣𝑣
𝐴𝐴
𝑃𝑃
𝑄𝑄
Stress
travels
down
Pull
Pull

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The reaction as Centripetal Force
This reversed pull travels back to
where the particle is. It acts on
the particle and changes its
direction so that the particle
turns to a new direction along
the circle and becomes a new
velocity vector.
𝑟𝑟
𝑣𝑣
𝐴𝐴
𝑃𝑃
𝑄𝑄
Pull
Pull

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The existence of the
Centrifugal Force
So the particle is not in a static
equilibrium, but in a dynamic
one. We call this force the
centrifugal force 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 in
opposition to the 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
thus incited. They are equal and
opposite in direction forming a
rotating but antagonistic pair
according to Newton’s third law
of motion:
𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
𝑣𝑣

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Transient existence
This centrifugal force appears as
an instant reaction to resist the
entrapment by the string. So its
existence is transient.
As soon as the string is
detached, the force is no longer
formed and the particle will run
away in a straight line. It
happens that its trajectory is
perpendicular to the string. So it
just leaves tangentially.
The centripetal force too. Having
no object to act on, it also
disappears.
𝑣𝑣

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The merry couple
So finally, we have the well-
known centripetal force:
𝐹𝐹⊥ = 𝑚𝑚𝑚𝑚 = 𝑚𝑚
𝑣𝑣2
𝑟𝑟
And the opposing centrifugal
force:
𝐹𝐹⊤ = −𝑚𝑚𝑚𝑚 = −𝑚𝑚
𝑣𝑣2
𝑟𝑟
The pair live happily ever
afterwards.

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THE CYCLICITY OF CIRCULAR MOTION
To be continued on: