Jaime Soto Figueroa writes:
Extremely Dangerous Gravitational Levitation Experiment:
Imagine a sphere or a disk of radius R[m] = 1[m], mass M[Kg] = 1[Kg] rotating around it's natural rotation axis pointing to the Earth mass center at a super high angular velocity of W[r/s] near the Earth surface, this is at some 6375500 [m] from the Earth Mass Center.
Let "K" be a proportion constant for the Moment of Inertia.
For a sphere K = 2/5
For a disk K = 1 / 2
In the case of the Sphere:
Sphere Moment of Inertia = M * R^2 * K = M * R^2 * 2 / 5
Moment of Inertia of a Disk = M * R^2 * K = M * R^2 * 1 / 2
G = Gravitational Acceleration = 9.8[m/s^2]
H = Distance to the Earth Mass Center = 6375000 [m]
Ep [J] = Potential Energy of the Sphere with respect to the Earth Mass Center
Ep [J] = M*G*H = 62475000 [J]
Ec [J] = Kinetic Energy of rotating Sphere
Ec [J] = M *K *R^2 * W^2
¿How much W[r/s] is needed to get Ep = Ec and get gravitational levitation at equilibrium of a sphere? (Or a disk)
I guess that to reach levitation at equilibrium, Ec must be equal to Ep
If Ec = Ep
Then
M*G*H = M *K *R^2 * W^2
W^2 = G*H/(K * R^2)
W = SQRT(G*H / K) / R
Let's see the case of the Sphere, with K = 2/5
If
Ec[J] = Ep[J] = 62475000 [J]
Then
W[r/s] = 12497 [r/s]
This means 1989 revolutions per second
Then the equatorial speed Se[m/s] of the rotating sphere would be
Se[m/s] = W * R = 12497 [m/s].
Note that the necessary equatorial speed is independent of the mass M and the radius R, so smaller spheres should have higher angular speeds.
To get levitation the mass M doesn't matter, the only thing is about the danger of explosion on experimenting ultra high-speed angular velocity, because the higher the mass M the higher the kinetic energy Ec.
Another shape may be a disk, with K = 1/2, but the important thing is to determine which shape is less fragile and less prone to explode, the sphere or the disk.
A disk with R = 1[m] should rotate at 1779 revolutions per second, thus the necessary equatorial speed would be 11178 [m/s], somewhat lower than that for the sphere.
Note that for any revolution body, sphere, disk, cylinder, ring, etc., the necessary equatorial speed is the same for any radius, so for smaller radius the angular speed should be higher, and note that the necessary angular speed is independent of both, mass M and radius R.
In any case the surface quality of the bodies must be premium mirror like, to avoid air resistance and melting with air friction, or the bodies should float in vacuum chambers, and that the material should be hard enough to cope with the strain and stress of centrifugal forces at that super-ultra high angular speeds.
¿Someone dares to do this experiment? One idea is mounting this gadget on top of a tower in the middle of a desert for if it explodes, then the debris fly away well over our heads.
One previous experiment is to measure if the weight of a rotating body decreases with angular speed, if this is true, then it is only a matter how to reach the necessary angular speed for gravitational levitation.
Please if you have budget to do this, invite me to participate. I have a design for this whole experiment for both cases, the disk and the sphere.
Yes, I admit that I may be crazy.
Thank you.
Jaime Soto Figueroa
http://www.matharts.cl/
Levitation?
