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## Abstract

When analyzing pendulum motion, textbooks avoid invoking centrifugal force. All upward acting forces are accounted for by the tension in the rod. This tension must however be greater in magnitude than gravity in order for a net upward force to be possible. The role of centrifugal force in both the simple pendulum and the conical pendulum will therefore be reexamined , and a connection with magnetic repulsion will be suggested.
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The Pendulum and the Magnetic Connection
Frederick David Tombe,
Northern Ireland, United Kingdom,
sirius184@hotmail.com
7thApril 2018
Abstract. When analyzing pendulum motion, textbooks avoid invoking centrifugal force.
All upward acting forces are accounted for by the tension in the rod. This tension must
however be greater in magnitude than gravity in order for a net upward force to be
possible. The role of centrifugal force in both the simple pendulum and the conical
pendulum will therefore be re-examined, and a connection with magnetic repulsion will
be suggested.
The Simple Pendulum
I. When a pendulum is hanging vertically in the static state, the downward force
of gravity acting on the bob is exactly balanced by a reactive upward acting
tension in the rod. When the pendulum begins to swing, unless the rod snaps,
the bob will rise upwards, hence indicating that the tension in the rod is now
greater in magnitude than the downward force of gravity. The additional tension
can only have been caused by centrifugal force pulling on the moving bob.
Levitation and the Inversion of a Conical Pendulum
II. In the case of a conical pendulum, the centrifugal force relative to the
fulcrum is no longer acting in the plane of motion. It has become one of two
mutually perpendicular components of the horizontal centrifugal force that acts
on the bob perpendicularly to the vertical axis. This resolved centrifugal force is
cancelled when it causes a reactive tension in the rod. The other component that
is perpendicular to it acts tangentially to the rod and in an upward direction,
hence opposing the downward effect of gravity. When the horizontal speed of
the bob is caused to increase, the bob will rise upwards.
It is not however expected that the conical pendulum would ever undergo a
sustained inversion whereby the cone points downwards and the bob circles
above a horizontal plane that contains the fulcrum. The reason why is because
above this plane the tangential acting centrifugal force component would now
be acting downwards.
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There is however another component of the horizontal centrifugal force,
this time acting along the line to the centre of the Earth. This is very much
weaker due to the large size of the Earth’s radius in comparison to the
apparatus. Nevertheless, if the bob should exceed 8km/sec, being the speed
above which the centrifugal force exceeds gravity, this will take the bob above
the fulcrum’s plane. If this happens though, the tangential acting centrifugal
force that is resolved from the horizontal centrifugal force, now acting
downwards, will very rapidly dominate and will severely limit the height that
the bob can levitate above the fulcrum plane.
Conclusion The Centrifugal Field is a Magnetic Field
III. In general when a body moves in a straight line, there will be a centrifugal
force relative to every point in space, . This is an indisputable geometrical
fact. Consider the moving body to be surrounded by concentric rings in a plane
that is perpendicular to the direction of motion. If these rings are solenoidal
magnetic field lines, then according to Maxwell, they would be vortex rings
pressing against each other with centrifugal force while striving to dilate . We
should therefore consider the likelihood that the centrifugal force field (or
inertial field) that surrounds a moving body is just another manifestation of
Ampère’s Circuital Law . If so, then it seems that a body moving in a straight
line is being squeezed from all sides, resulting in an inertial pressure (kinetic
energy) which increases with speed, while dropping off with distance as we
move away from the body. From orbital theory we can conclude that the drop
off will obey an inverse cube law in distance. When the moving body
encounters a physical constraint, or when the centrifugal pressure field is
undermined by a gravitational tension field, a pressure imbalance will occur and
the path of motion will curve.
The magnitude of any centrifugal force relative to a point on a tangent to
any of the concentric circles (field lines) will be a resolved component of the
centrifugal force at the point where the tangent touches the circle. Likewise the
centrifugal force to any point on a cylinder extended from any circle will be a
resolved component of the centrifugal force to the original circle.
References
 Tombe, F.D., “The Centrifugal Force Argument” (2014)