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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, [1]. 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 [2]. 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 [3]. 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

[1] Tombe, F.D., “The Centrifugal Force Argument” (2014)

http://gsjournal.net/Science-Journals/Research%20Papers-Mathematical%20Physics/Download/7180

[2] [Clerk-Maxwell, J., “On Physical Lines of Force”, Philosophical Magazine, page 171-

172, Volume XXI, Fourth Series, London, (1861)

http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf