In modern physics it is considered, that in a rotating body the pulses mv compensate each other. Hence the total pulse of a rotating body is equal to zero. It means that the weight of a body does not increase at rotation. At a level of the pulses it is correct, but without attention there is a centrifugal acceleration.
As a result of this ignoring the moment of inertia is compensated too. It turns out the paradox that the body has more weights before it will start to rotate I = mR2. But during rotation this "superfluous" weight disappears somewhere completely.
There is a question: if the weight of a body "increases" as a result of growth of linear speed why the weight cannot increase as a result of centrifugal acceleration?
As such result is demanded with a principle of equivalence of A. Einstein.
Even if the elementary particle has a spin, why a massive rotating body cannot have own moment of a pulse which is caused by centrifugal acceleration instead of tangential speeds?
This elementary growth of weight as a result of rotation of a body about the axis is not taken into account in modern theories. The existing theory considers only the general influence of "cross-section" force on acceleration of a body as a whole, and centripetal acceleration inside a body appears not in a field of vision. In result there is "deficiency" of weight. But this deficiency is taken into account by a principle of equivalence. According to this principle, on the person placed in a centrifuge, the same force operates as though he falls from height .
But acceleration of a falling body is linear, and acceleration of a rotating body – centrifugal. And centrifugal acceleration exists even then when speed of rotation does not vary, and at linearly moving body the acceleration "appears" only at change of speed of movement. So centrifugal acceleration is "constants" at an invariance of speed of rotation. There is a question: whether can make this constant acceleration work constantly, without change of speed of rotation of a body?
For levelling the above-stated distinctions, the dynamics of a rotating body is described by special formulas.
But these formulas result in illogical conclusions: at the description of rotary movement of a body, it is considerd that the equivalent of force F is the moment of force M = FR where R - the radius of a rotating body, and is an equivalent of weight is the moment of inertia I = mR2/2,
Accordingly the kinetic energy of a flywheel is ---E=Iω2/2, where -- -ω - frequency of rotation of a flywheel
If to calculate capacity of a flywheel on his kinetic energy by analogy to linearly moving body, we receive ignoring of centripetal acceleration. Р = I2ω/2 t = mR2/2* v2/R2/2 t = mv2/4t. i.e. kinetic energy of a flywheel and therefore capacity is in 2 times less than of linearly moving body. Here the difference of linear speeds of an axis and a surface of a flywheel is taken into account - therefore average speed V/2 is received . But why thus the result of this difference of speeds is ignored? - "constant" centrifugal acceleration, which existence does not depend on instability of linear speeds of a flywheel?
Value and role of centrifugal acceleration become clear at generalization of other special formulas:
Generally the capacity of a body moving with constant speed is: P = F•v•cos α where α --there is a corner between vectors of force F and speeds v. But this corner matters only at curvilinear movement. Directions of vectors of speed and force coincide both at rectilinear and at rotary movement. I.e. α =0 and accordingly cos α =1. hence the considered formula will be written down in more simple kind.
Certainly, in a rotating body vectors of speed and centrifugal force are perpendicular. But it is not necessary to transfer logic of simple curvilinear movement on this fact. At curvilinear movement vectors of direction - speed and acceleration "prevent" each other. Each vector "pulls" in an theyr own direction. But at rotary movement the vector of tangential speed in any way does not prevent centrifugal force. Even on the contrary - it strengthens its with effect of the lever. Therefore at rotary movement it is possible to measure capacity of a flywheel under the formula:
P=Fv = m*a*v
In case of a rotating body a=v2/R, the equivalent of force F is the moment of force M = F R where R - the radius of a rotating body, and an equivalent of weight is the moment of inertia I = mR2/2,
If to calculate capacity of a rotating body under these formulas
P = F V = mR2/2, * v2/R* v
we receive a power unit---Н*м4/с3---here meter in the fourth degree corresponds not quite to the representations about "organic" components of capacity.
I.e. this formula is wrong in essence. Since it turns out, that a power unit is-----Н*м4/с3, instead of Н*м2/с3
Thus in the general formula of Newton F = mа it is necessary to apply only one special size a=v2/R,
Hence the capacity of a rotating body should be calculated under the formula: P=m v3/R. since only in this case it turns out, that a power unit is-----Н*м2/с3, instead of Н*м4/с3
For best accuracy it is possible to count, that here v is the average speed of a rotating body, instead of his surface.
The same average-speed should be taken into account at comparison with dynamics of linearly moving body:
In a case of linearly moving body---a = Δ v / Δ t: i.e. P = m v2 / 2t
According to a principle of equivalence, the capacity of linearly moving and rotating body of the same weight should be equal:
m v3/R = m v2 / 2t
But it is possible, when----v/R =1/2t.
I.e., if R <2 v t then capacity of a rotating body is more than capacity of linearly moving body of the same weight with the same speed. I.e. capacity is increased not due to increase of radius of a rotating body, but on the contrary - as a result of reduction of this radius at preservation of weight.
Except for that the capacity of a linearly moving body is created from the square of speed Р = mV2/2t, but a rotating body - only from a cube of speed É = mV3/R.
i.e. capacity of a flywheel is equal to capacity of linearly moving body, when R=2V* t. But 2V t is huge figure. Such radiuses does not happen in real technics. If linearly moving body with a speed 1м/с and weight 1kg. stops i.e. spends the kinetic energy for 1 second, developing thus capacity: Р = mV2/2t=1*1м/с2=0,5ватт, then the flywheel should have radius R=2V t = 1м/с2 *с=2 meter for development of the same capacity . If a disk in weight 1 kg to flatten out on 2 meter radius, so such thin sheet of a foil will turn out, which will become torn at rotation. But at reduction of radius of this flywheel the potential capacity increases. However it does not mean, that the thin and long core from the same steel has the boundless big capacity. Escalating of capacity occurs as a result of a difference of radiuses between a surface and an axis of a flywheel, instead of the "reforging" a disk in a core.
Thus at normal - i.e. naturally possible technical parameters
mV2/2t <mV3/R.
Apparently, the dynamic characteristics of capacities of rotating and linearly moving bodies differ essentially: from the formula mV2/2t it is clearly visible, that for realization of the capacity linearly moving body should will stop in time t, transferring thus the energy mV2/ 2 to other body. But the rotating body does not require to stop. On the contrary: Apparently from the formula mV3/R - capacity "is constant" and even is directly proportional to the speed. I.e.as far as the speed of rotation will more, so much work will be made by flywheel , not stopping thus.
The advantage of centripetal acceleration becomes clear also at generalization of a component of force of a rotating body:
In that specific case, as it was marked, in a rotating body:
F=F R,
m = m R2/2,
a=v2/R
But if to this private dynamics of a flywheel we apply the general
Newtons law F = mа it turns out:
F R = mR2/2* V2/R
F = mV2/2---and it is the formula of kinetic energy (instead of forces) of linearly moving body irrespective of his form.
If to calculate capacity of a rotating body with this formula
É = F V = mV3/2 - we receive a power unit---Н*м3/с3-
Here we receive cubed meter as against the above-stated calculations where the meter turns out in 4-th degree .
Thus in the general formula of Newton F = mа it is necessary to apply only one special size a=v2/R, as the moment of inertia and the moment of force "are thought up" groundless. At least, they are superfluous at calculation of capacity of a flywheel . If they are not superfluous, then it is received a new power unit -----Н*м3/с3 which again proves, that the body develops at rotation the more capacity, than at linear movement with the same speed.
These inequalities are applied in several updatings of "perpetuum mobile". By theoretical analogy are already developed both electrodynamic and aerohydrodynamical variants. In electrodynamic variants theoretically it turns out in 50 times more energy, in mechanical variants up to 10 times more energy, and in aerodynamic variants only in some times.
To prove the above-stated theoretical hypothesis is possible at simple experiment with the help of the simple device. It will consist of the vertical rack (1) on which with the help of the motor the horizontal axis (2) rotates. On the ends of this axis two spheres of identical weight and diameter (3а and 3 б) are hanged. These spheres rotate too with the help of electromotors (4а and 4б). Spheres are suspended on rotors of these motors.
On the first experiment the spheres do not rotate about the axis. But that horizontal axis, on which they are suspended, rotates. In result of it spheres deviate from an axis on the certain corner.
At the second experiment the spheres already rotate about the axis. That horizontal axis on which they are suspended rotates too. If at rotation of spheres about the teir axis their weight increases, then the corner of a deviation of these spheres will be distinct from a deviation at the first experiment.
With this device it will be possible to establish the factor of dependence of a corner of a deviation from speeds of rotation.
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