Mass responded to an attraction force at its center. The attraction force had two manifestations, the gravitational force on radial motion and the inertial force on rotational motion. The inertial force caused tangential motion perpendicular to the radius. The spiraling motion had a path with positive curvature away from linear tangential speed (i.e. an attraction force toward the center of rotation). However, the mass at the surface of the rotating system moved to less curvature (decelerated curvature) for both the small mass (rotating system) as well as the large mass (Earth), while increasing rotational velocity (tangential speed).
The radius of the inertial system increased with increasing inertial force (torque) until its surface had the minimum curvature allowed by the apparatus, which was at its equatorial surface. The spiraling motion was called equitation. Additional twist energy added to the axis of the horizontally rotating system(internal torque), increased angular velocity (rotation rate) without further vertical changes in the Earth frame of reference or curvature deceleration at the surface of the rotating system.
The gravitational force is known to cause radial motion of a small mass with accelerated speed toward the center of the large mass. This linear motion has a path through increasingly positive curvature of space (accelerated curvature) using the large mass as a frame of reference.
When the inertial attraction force (torque) was great enough, the intrinsic angular momentum of the small mass caused the creation of a new inertial mass system. The spiraling motion was independent of mass. This new system had its own frame of reference independent of the Earth. Angular momentum directed the gravitational force to the center of rotation. The rotating system center of mass moved away (“levitated”) from the Earth’s center of mass.
When the twist energy was removed, the gravitational attraction between the two centers of mass caused them to move toward each other. From their separation in the rotating state they moved until the rotating system mass was at rest with respect to the Earth’s surface. The rotational inertia motion was compared to precession motion of a single frame gyroscope.
Key Words: gravity, angular momentum, inertia, force, torque, center of mass, rotational velocity, rotation, acceleration, precession, gyroscope, levitation.
A spinning system was set up for doing experiments to demonstrate the rotating mass properties of inertia, gravitation, rotation, and precession. The carousel like apparatus allowed rotational “inertial mass” effects to be separated from those of gravitational mass. Additional experiments were run with single frame gyroscopes to confirm principles.
Howard Kober’s desire is to understand the created universe. He studied Classical Physics, Quantum Mechanics, and Relativity in his office and laboratory for over 50 years. He has done extensive experiments to clarify understanding and obtained patents in the field of rotational inertia, precession, and angular momentum.
Dale Crouse’s desire is also to understand the created universe. He studied chemistry, receiving his doctorate (Ph.D.) in 1970. Then, while supporting his family and seeking understanding of how the business enterprise works, he continued to broaden his study of the universe. Recently his interest has focused on understanding the unity between physics, chemistry, and life.
Anthony Talbot’s talent is as a scientific illustrator and cartoonist. Tony is centering his academic study on anthropology to gain credentials as a scientist. He has learned Wolfram Research’s Mathematica® to give mathematical accuracy to the theory and he also helped with the rotation experiments.
Levitating Mass® - copyright January 11, 2005
Experiment
Description Summary
Equitation
Rotation – Flexible Spoke & Lead Balls
Precession
Rotation – Single Frame Gyroscope
Mass
Distribution and Rotation Rate
Experiment Description Summary
Lead
Balls Spin Experiment
Starting with the balls orbiting the spindle, Fig 1, the centers of mass for the pair of balls, 1h and 3h, were in a plane parallel to the Earth (horizontal) that included the pivot point, P. The center of inertial mass for the rotating system of the two balls was also at P. The balls were separated by the diameter, dspin, and the tethers 1hT1 and 3hT3 were stiff. After stabilizing at 300rpm with a given energy and the rotation CounterClockWise (CCW) looking up from the Earth toward the rigid pivot point, an increase in energy to the spindle apparatus was converted into faster rotational velocity of the balls. The rotation rate was proportional to the amount of energy. Alternately, if the energy of a specific configuration of balls was held constant, but the length of the tether shortened, the balls rotated at faster than 300rpm and the rate (after stabilization) was inversely proportional to the tether length.
At a minimum energy supplied when the balls were rotating in the horizontal plane their rotational velocity was 300rpm, independent of their mass. The mass was varied from two ½ oz balls (1 oz total) to four balls at 48 oz each (12 pounds or 192 oz total). With further careful reduction in energy to the fan motor the spinning system moved through the transition zone between horizontal and vertical where the rotation rate slowed and the balls fell from the horizontal to the vertical. The rotating balls could be sustained at intermediate energy input, rotation rate, and specific ball & tether angle. This transition zone was from 300 rpm and an angle of 900 through energies that gave a minimum stable rotation rate of about 160-180 rpm and balls & tether angle down to about 650 to the spindle. This stable rotation rate and specific angle (or curvature to the path and circumference traveled per cycle), were also independent of the lead ball mass. Below these energies, the rotating system in the transition zone became unstable and the balls slowed their rotation and fell to vertical, an angle of 00, due the effects of friction and Earth’s gravity. The tethers remained stiff during the transition zone as if the balls could not advance or decline vertically or rotationally from a line extended out from the attachment point (T) that goes back through the platform to the pivot point (P). Changing the density of the balls from lead to plastic with the same dimensions, gave similar rates and angles. When dspin was increased from 20.7 cm to 33.2 cm by adding a bar above the platform, the balls became horizontal ~215 rpm instead of ~300 rpm.
In the vertical orientation, the balls were still orbiting the spindle at 60 rpm (once per second), the centers of mass for the pair of balls, 1V and 3V, are in a plane parallel to the Earth that includes the point CM(I). The center of inertial mass for the spinning system of the two balls was almost at CM(I) (slightly higher), the “at rest” position. The balls were separated by the diameter, drest, and the tethers 1VT1 and 3VT3 were stiff. Continuing to reduce energies, the balls slowed their rotation and came to a halt due to friction.
Key observations of equitation transition experiment from “at rest” to a stable state of levitation with added twist energy and then slowly back to “at rest” when the twist energy was removed:
- Tether portion of the rotating spoke rose as twist energy was added to the axis.
- All spokes reached horizontal at 300 rpm independent of amount of mass or mass density attached.
- The radius of the rotating system surface increased as the rotation rate increased.
- The tethers were always stiff at all times whether mass was attached or not.
- The tethers only bent at the spoke branch point in a vertical angle, not horizontal, keeping equal spacing between the tethers independent of mass on the tether.
Four 3lb (48oz) or a total of 12 pounds of balls are spinning at 300 rpm
Gyro on String or Pedestal Experiment
The single frame gyroscope was rotated by pulling a wound string on the shaft[1]. The gyro was suspended at one pole either from the ceiling by a string or from the floor by a pedestal. In both cases when the rotation of the gyroscope rotor about its spin axis was between 300-450 rpm, the spin axis rotated (precessed) in the horizontal plane around the flexible pivot point at the North Pole of the gyro. As the rotation of the rotor gradually slowed down due to friction, the spin axis fell as far as possible toward the vertical from the horizontal while continuing to precess around the pole pivot point. When the direction of the rotor rotation was ClockWise (CW), the precession rotation was CounterClockWise (CCW). When the rotor stopped spinning, the gyroscope hung motionless from the string with the axis vertical.
Precession
Explanation of Precession is based around a description of Fig 1.14 in The Gyroscope Applied by K.I.T. Richardson. {redrawn as Fig 3 in this document}
Fig 1.14 (Fig 3 here) ‘A single frame gyroscope when supported at N by a string will precess as shown at S by the dotted [red] arrow, due to the pull of gravity shown by the vertical [dotted black] arrow’.
A gyroscope precesses horizontally when the minimum angular momentum of the rotor is spinning less than 450 rpm near the surface of the Earth. Precession can be explained as the result of three torques, each torque manifested in one dimension of three dimensional space and all taking place at the same time. The Rotation Torque (1), the Gravitational Torque (2), and the Precession Torque (3) cause the inertial system to come into equilibrium with the gravitational system.
String Experiment
Three torque explanation applied to the single frame gyroscope.
The first torque (Rotation) {“intrinsic” inertial force torque} involves the spinning rotor creating angular momentum [blue cyclic arrow in Fig 4], and directing the gravitational force of the rotor to its axis. In the figure the rotor mass is shown in the form of 4 balls attached by spokes to the spin axis at the center of inertial mass CM(I) (red cross hatched circle).
The Rotation Torque was applied to the surface mass on the rigid spokes of the gyroscope. This caused curved motion in the y,z plane [i.e. surface mass moves from -z axis (1), to y axis (2), to z axis (3), to -y axis (4)]. The torque was applied in a tangential direction at the surface of the rotor, which was perpendicular to the attraction force communicated through the radial spoke from the center of inertial mass, CM(I) (red cross hatched circle). The Inertial Force was responsible for this torque.
The second torque (Gravity) {gravitational force torque} results from the Earth’s gravity, CM(E) (the attraction force located in the center of Earth’s mass) pulling down on the gyroscope [green arrows] that was in a horizontal position, and was supported at one end by a string.
The Gravity Torque was applied at the end, S, of the gyro’s spin axis[2]. The Gravitational Force was responsible for this torque. This caused curved motion in the x,z plane (i.e. surface mass moves from -x axis to -z axis) . The torque was applied in the direction toward the center of gravitational mass (Earth) from the attraction force at the center of gravitational mass[3], through a complex path. The gravitational attraction force was communicated to the flexible branch point, N, through a path of molecules in the Earth mass system including the string[4]. It continued perpendicular (horizontal) from the branch point, N, through the inertial mass system by a path of molecules in the axis and then distributed at right angles to mass at the surface of the rotor by the molecules in the spokes, and finally continued along the axis to S.
The third torque (Precession) {“orbital” inertial force torque}occurs as a result of gravity pulling downward on the gyroscope, and the angular momentum of the rotor moving at right angles to this pull, that starts precession. As a result of this new rotation the gravitational force of the rotor (see footnote 3) will now be directed to the string, the center of this new rotation {branch point N in the figure}, or precessional mode.
The Precession Torque was also applied at the end, S, on the gyro’s spin axis. The Inertial Force was responsible for this torque in response to the Gravitational Force. This caused a cone shaped spiral curved motion for the axis {Fig 5, 6, & 7} in the x,y plane (i.e. surface mass from branch point N rotates from -x axis to y axis, to x axis, to -y axis) while the Rotation axis [red] moves through a right angle between horizontal[5] and vertical[6]. The torque was applied in a tangential direction at the axis end, S, which is perpendicular to the attraction force from the center of inertial mass and also perpendicular to the gravitational torque.
The Precession Torque 3 depends of the direction of rotation and will continue until the gyroscope’s rotation stops, and also depends on which end of the Rotation axis the string is placed. If the rotor rotation is clockwise looking from N, then the precession rotation is counterclockwise around the string at point N (as shown in Fig 5 looking up from the Earth). If the rotor rotation direction is reversed or the end where the string is attached is reversed i.e. attached at S vs N, then the precession will be clockwise. The radius of precession rotation was larger than the radius of rotor rotation (1 ¾ inch versus 1 1/8 inch) meaning the curvature of the rotation surface (S circumference) had less curvature for Precession torque (third) than the curvature for Rotation torque (first).
Equitation
A rotating mass system equitates[7] vertically when the minimum angular momentum of the rotor is spinning less than 450 rpm near the surface of the Earth.
Equitation can be explained as the result of three torques, each torque manifested in one dimension of three dimensional space and all taking place at the same time. The Rotation Torque (1), the Gravitational Torque (2), and the Equitation Torque (3) cause the inertial system to come into equilibrium with the gravitational system. Equitation motion appears as levitation.
Lead Balls Experiment
Three Torques explanation applied to the lead balls experiment
The first torque (Rotation) {“intrinsic” inertial force torque perpendicular to axis} was applied to the surface mass on the flexible spokes of the rotating mass. This caused curved motion in the y,x plane (i.e. surface mass moves from x axis (1), to -y axis (2), to -x axis (3), to y axis (4)). The torque was applied in a tangential direction at the surface of the rotor, which is perpendicular to the attraction force communicated by a complex path of molecules (C to P to T to Ball in Fig 8) through the flexible spoke from the center of inertial mass, CM(I) (red cross hatched circle). The Inertial Force was responsible for this torque.
The second torque (Gravity) {gravitational force torque} was also applied to the surface mass of the flexible spokes. The Gravitational Force was responsible for this torque. This caused curved motion in the x,z plane (i.e. surface mass moves from -x axis to -z axis) at the branch point, T, for the flexible spoke. The torque was applied in the direction toward the center of gravitational mass (Earth), through a complex path. The gravitational attraction force was communicated through a path of molecules from the Earth system to the rigid spin axis (spindle) and then the rigid point, P, the Pivot point for the inertial mass. Then the gravitational force was communicated in a perpendicular direction (horizontal) to the flexible branch point, T, and continued through the flexible spoke to the ball at the surface of the rotor.
The third torque (Equitation) {“intrinsic” inertial force torque parallel to axis} was also applied to the surface mass of the flexible spokes. The Inertial Force was responsible for this torque creating a Levitation Force opposite to the Gravitational Force. This caused a cone shaped spiral curved motion for the spokes[8]{Fig 9, 10, & 11} in the x,y plane (i.e. surface mass connected at branch point T rotates from x axis (1), to -y axis (2), to -x axis (3), to y axis (4)) while the flexible spoke moves through a right angle between horizontal[9] and vertical[10]. The torque was applied in a tangential direction at the end of the spoke, which is perpendicular to the attraction force from the center of inertial mass and also perpendicular to the Gravity Torque. Since the Rotation Torque and Equitation Torque are applied perpendicular at the surface, the center of inertial mass, CM(I) (red cross hatched circle), levitates from C to P when the inertial force is turned on.
When the spoke reaches the equatorial plane, the third torque pushing the balls to the surface with the least curvature for the Inertial Force no longer causes vertical motion. The second torque was opposite to the third torque at all times while the rotor slowed down and stopped, and the rotating mass on the spoke fell toward the Earth in the Lead Ball experiment. Different, but similarly, in the Gyro experiment the second torque was perpendicular to the third torque at all times while the rotor slowed down and stopped, and the rotating system axis fell toward the Earth (Fig 12). The Inertial Force causing the equitation and precession torques, created a force in the opposite direction to the Gravitational Force and motion of the rotating mass, which diminished to zero as the rotation stopped. In precession the axis of the gyroscope moves, whereas in equitation the plane of the rotating mass at the surface spirals out toward the equator. At 300 rpm (5 revolutions per second), the precession or levitation force created by the rotating inertial mass system balanced the gravitational force of the Earth and the rotating mass became an independent mass system or frame of reference. The Precession Force angle to the spoke increased from zero when at rest becoming perpendicular to the Inertial Force toward the spin axis when the Inertial System was independent (horizontal).
Fig 12 – Precession or Levitation
Forces
The Levitation (Equitation) Force angle to the spin axis in the flexible spoke increased becoming perpendicular to the Inertial Force when the Inertial System was independent (horizontal). Using “Gravitational Force” and “Inertial Force” as an attraction force located at the center of mass for Earth and the Rotating System respectively allowed an interpretation for the lead ball as well as the string suspended gyro experiments.
The path integral concept was used to track how the gravitational force was transmitted through mass atom by atom, or molecule by molecule. Only electrons of the subatomic particles have orbital angular momentum in atoms and are therefore carrying the gravitational message through the mass. The “path” result allowed linking together conceptually both experiments: where the rotating spin axis tethered to lead balls was perpendicular to the plane of the Earth, and the gyro spin axis held by the string was parallel to the plane of the Earth (Fig 12).
In all cases the torques 1 & 3, caused by the Inertial Mass, are perpendicular to the radial line toward the center attraction force of Inertial Mass, whereas torque 2, caused by the Gravitational Mass (Earth), is in the same direction as the radial line to the center attraction force of Gravitation Mass.
If the attachment to Inertial Mass was at the center of its mass, there would be “no gravity torque” and the mass would fall in a straight line to the surface of the Earth[11]. Because in these experiments the attachment is at a flexible “branch point” separated by a lever arm from the center of Inertial Mass, there is a torque. That the flexible branch point was at the end of the spin “axis” in the String experiment, and was along the “spokes” in the Lead Ball experiment was very interesting. The spin axis is known to keep its integrity including its absolute orientation in space. The flexible spokes also maintained an axis like character, linear between the surface and branch point along the spoke, and the whole spoke acted as a unit like the spin axis. This did not change the theoretical explanation, however, based on the attraction force at the frame of reference center, but did suggest new terminology was needed (equitation versus precession).
The radial dependence of rotation rate in the lead ball experiments had five seeming conflicting characters: (1) increasing rotation rate with increasing radius for equitation (or levitation) with increasing energy - Table IIa); (2) increasing rotation rate with decreasing radius of the platform – Table V; (3) increasing rotation rate with decreasing radius in the skater experiment (reducing the distribution of mass in space at constant energy – Table III); (4) increasing rotation rate at constant radius with increasing energy above equitation zone (radius or spoke constrained by structure of rotating mass); and (5) Up to the peak rotation rate, 215 rpm, an elastic tether (rubber band) in the flexible spoke[12], gave increasing rotation rate with increasing radius (Table VI) with increasing energy. In all cases the center of inertial mass moved to the least curvature for both the Inertial System and Gravitational System at a given energy and physical constraint due to structure.
There was
complexity in the results due to different experimental configurations that may
have introduced asymmetric friction effects like binding in the tether, or the
location of the break points. Balls on
the long spoke and the short spoke seemed to affect each other. There seemed to be vibrations or harmonic oscillations
both in the plane and along the axis in some experiments with very small mass
(1/2 oz). However, increasing rotation
with changing twist energy supplied by the fan motor during the equitation
stage of spin up or slow down seemed to give a consistent tangential velocity
of ~11 ft/sec (10.7-11.8 bolded italic in the Tangential Velocity
table) independent of mass or mass density when the mass just reached
horizontal and the inertial system became an independent frame of reference.
|
Spinning
Ball Experiment - Tangential Velocity |
||||||
|
|
calc |
Rotation |
|
calculated |
||
|
Radius |
2πR |
Rate |
|
velocity |
velocity |
velocity |
|
cm |
cm |
rpm |
Experiment - Table |
cm/min |
ft/sec* |
light
speed |
|
10.34 |
65 |
304 |
Skater - 2oz - Table III |
19,800 |
10.8 |
0.0000011% |
|
6.80 |
43 |
448 |
Skater - 2oz - Table III |
19,141 |
10.5 |
0.0000011% |
|
16.06 |
101 |
214 |
Skater - 2oz - Table III |
21,600 |
11.8 |
0.0000012% |
|
13.04 |
82 |
303 |
Skater - 2oz - Table III |
24,826 |
13.6 |
0.0000014% |
|
16.06 |
101 |
196 |
Skater - 16oz - Table III |
19,800 |
10.8 |
0.0000011% |
|
13.04 |
82 |
279 |
Skater - 16oz - Table III |
22,859 |
12.5 |
0.0000013% |
|
|
|
|
|
|
|
|
|
10.34 |
65 |
480** |
Repulsion - 1oz- Table I |
31,185 |
17.1 |
|