## Gravity and Centrifugal Forces

First, consider the movement of a mass (a sphere or body of water) moving in a circular path around the inside wall of a hollow cylinder. Centrifugal forces always press radially outwards while Gravitational forces always act straight downwards. Figure 07.05.01 shows diagrams of three situations.

A partial plan view of such a cylinder is shown in grey. This cylinder has a radius of 100 cm (R100). Along its inner wall, mass M is moving at a speed of 3.13 m/s (see arrow V3.13). This mass is continuously pushed inwards by the cylinder. This inward acceleration A can be calculated by the formula Speed squared divided by Radius, in this case, with 3.13 m/s at a radius of 1 m, acceleration A = (3.13)2 / 1 = 9.8 m/s2.

Matching that inward acceleration is the outward centrifugal force of that mass. That centrifugal force (A9.8) is shown as the red vector in the diagram. Gravitational acceleration is also about 9.8 m/s2, and is shown here as the green vector (G9.8) in the diagram, acting vertically downwards. The resulting force is shown as the blue line in the diagram. If the cylinder wall were replaced by the inside surface of a cone with a 45 degree inclination, then the mass would rotate at the same speed, maintaining a constant height.

Now, consider the middle diagram. Here, the radius distance to the wall is only 24 cm (R24) and the mass is only moving at 1.5 m/s (V1.5). The inward, or "centripetal" acceleration produced is A = 1.52 / 0.24 which is 9.8 m/s2 so, here again, the centrifugal force (A9.8) corresponds to acceleration under gravity (G9.8). Consequently, the diagram of the resolution of forces matches that of the previous diagram.

So whenever a mass completes one rotation in exactly one second, the centripetal (inward) acceleration is the same as acceleration under gravity. At a radius of 1 m, the circumference is about 3.13 m and so the speed is about 3.13 m/s for one rotation per second. At a radius of 0.24 m, the circumference is about 1.5 m and so one rotation per second requires a speed of 1.5 m/s, and so identical results are produced. Whether this happens to be a pure coincidence or due to some other cause, is discussed later in the section entitled "Aether Physics".

In the lowest section of Figure 07.05.01, a rotation at this same speed of 1.5 m/s (V1.5), but this time at the shorter radius of, say, 16 cm (R16) produces a stronger inward acceleration given by A = 1.52/0.16 which works out at about 14 m/s2. As the force diagram shows, this results in the mass rotating along a circular track which is higher up than the previous tracks. This can be seen in action when coffee in a cup is being stirred vigourously.

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