The New First Law of Classical Dynamics

Scientific Paper
Title	The New First Law of Classical Dynamics
Read in full	Link to paper
Author(s)	Philipp M Kanarev
Keywords	first law of dynamics, inertia, force of inertia, uniform motion, unbalance, centrifugal force
Published	2009
No. of pages	8

Read the full paper here

Abstract

Classical theoretical mechanics on a way of modernization. Classical dynamics studies movement and interaction of material bodies. Its bases have been incorporated by Newton in 1687 in him ?The Mathematical beginnings of natural philoso-phy?. The first law of dynamics describes rectilinear and uniform ( ) movement of a body.

Overview

Ph. M. Kanarev's short 2009 paper attacks the first law of dynamics — Newton's law of inertia — at its most familiar point: the statement that a body in uniform rectilinear motion has zero net force acting on it. Kanarev denies this. His replacement, which he names outright as "Kanarev's law", is that the sum of the forces working on the moving body is never equal to zero.

The mechanism he proposes is a reinterpretation of the d'Alembert inertial force. In the standard treatment, a body accelerated by an applied force F is described as experiencing an inertial reaction F_i = −ma opposing the acceleration, a bookkeeping device that makes the dynamical problem look static. Kanarev takes this inertial force to be physically real and, crucially, claims that when the body stops accelerating and settles into uniform motion the inertial force automatically reverses direction and becomes a driving force — a "passive force" that thereafter carries the body along. Uniform motion is therefore not force-free at all: the inertial force sustains the motion, and whatever engine is present has only to cancel the resistance.

The paper's second half draws a practical, and far more contentious, consequence from this: if inertia can drive a body, then the inertial moments of rotating unbalanced masses can be used to drive a shaft, reducing the electrical energy an electric motor must consume. Kanarev presents an over-unity claim from a device built by the Russian engineer Linevich Edvid Ivanovich, with a table reporting output powers exceeding input by factors of roughly 14 to 18.

The argument

The four phases of a car journey

Kanarev's exposition is built entirely around a worked example: an automobile passing through accelerated motion (segment OA), uniform motion (AB), coasting with the transmission switched off (BC) and renewed acceleration (CD), compared throughout with an asteroid moving uniformly and rectilinearly in empty space.

During acceleration, the kinematics are V = a·t and Newton's second law gives F = ma, with the d'Alembert inertial force F_i = −ma directed against the acceleration. Kanarev notes that if these are simply added one gets

F + F_i = 0

and remarks that this "obviously contradicts the second law of dynamics", which describes the accelerated motion of a rocket or satellite in space where there is no resistance. He treats this as a real contradiction requiring resolution, not as a formal identity.

Separating the two accelerations

His resolution is to insist that the acceleration appearing in the inertial force is not the same as the acceleration of the body. For the accelerating car he writes the force balance as

F = F_i + F_C, or ma = ma_i + F_C

where F_C is the resistance. Hence F_i = ma_i = F − F_C, and the "inertial acceleration" a_i is strictly less than the full acceleration a — it is the acceleration the body would have in the complete absence of external resistance. Kanarev concludes that the true magnitude of the inertial force can only be measured either with no resistance present or by subtracting all resistances from the applied force.

The reversal at the transition to uniform motion

The pivotal claim is that at the transition from accelerated to uniform motion the inertial force, having until then opposed the motion, "automatically changes the direction on opposite and turns valid, promoting its movement". The equation for the uniform segment then reads

F + F_i = F_C

whose meaning, Kanarev says, is that "uniform movement of the automobile is provided with force of inertia F_i, and the force F generated by the engine of the automobile overcomes all external resistance". The sum of the forces on the body is manifestly not zero — hence the new first law.

The asteroid is used to answer the obvious objection. How did a body in free uniform motion acquire an inertial force? Because, Kanarev argues, at some point in its history an external force accelerated it, generating an inertial force directed against its motion; when the external force disappeared, the inertial force flipped direction and has been carrying the asteroid along ever since. He calls this a passive force, because the body moves under it without accelerating. The same reasoning is applied to a plane in level flight: its engines only overcome drag, while the inertial force does the propelling.

From inertia to fuel economy and over-unity

Kanarev asks which force is responsible for fuel economy in a car and answers "force of inertia" — noting that on the coasting segment BC the car travels while burning no fuel. He then asks whether the inertial force arising in rotation could be used to save the electrical energy consumed by a motor, and observes that centrifugal inertial force does not reverse direction when the driving moment is removed.

For a motor shaft the analogue equations are ω = ε·t during run-up, with

M_Z = M_i + ΣM_C (accelerated rotation, M_i = ε·I_Z)

M_Z + M_i = ΣM_C (uniform rotation)

Because both the motor moment M_Z and the inertial moment M_i appear on the same side in the uniform-rotation equation, Kanarev argues one may deliberately increase the share carried by M_i and decrease the share carried by M_Z, and so unload the motor.

The unbalance device

The scheme (Kanarev's fig. 2, attributed to Linevich) is an electric motor driving a central gear meshed with two gears carrying deliberate unbalances D₁ and D₂, together with an overrunning clutch. The projections F_x and F_y of the centrifugal inertial force of the two unbalances form couples, and Kanarev writes the two component moments M₁ and M₂ explicitly as functions of the unbalance mass m, the radius r of rotation of the unbalance centre of mass, the distance R from the shaft axis to the unbalance axis, and the angular speed ω. Both are proportional to mω² and vary as sin ωt and sin ωt cos ωt. M₁ is taken with a plus sign because at the initial moment it promotes rotation of the motor shaft, M₂ with a minus sign because it opposes rotation, and their sum M = M₁ + M₂ is the "law of change of the moments of these pairs". Kanarev says this summed moment reproduces, as scalar quantities, the "continuous deformed sinusoid" measured experimentally (his fig. 6). The essential asymmetry he points to is that the positive amplitude of the moment pulses, and the angle ωt₁ over which it acts, both exceed the negative amplitude and its angle ωt₂. The overrunning clutch is there to cut off the negative part of the pulse, so that only the positive pulses reach the load; when those pulses exceed the resistance moment they relieve the motor shaft, which then runs essentially at idle. Kanarev adds that at high shaft speed, backlash and elastic deformation in the drive perform the clutch's role and the clutch becomes unnecessary — a theoretical consequence he says the inventor confirmed experimentally.

The reported measurements

The paper reproduces Linevich's table for a 500 W motor driving a 6 kW generator rotor (Austria, January 2009):

№	U, V	I, A	P(input), W	P(output), W	Keffect, %
1	19.10	18.00	344	6131	1782
2	19.30	20.00	386	6080	1575
3	19.60	22.00	431	6160	1429

Kanarev states that the electrical energy consumed falls "in 10 and more times".

The concluding paragraph extends the claim well beyond mechanics: the law of transformation of the inertial force, he says, "operates uniform and rectilinear movement of photons", a topic he refers to his own multi-volume Foundation of Physchemistry of Microworld.

Assessment

The paper is at its strongest as a pedagogical complaint. Students really are taught both that F = ma and that the d'Alembert force F_i = −ma acts on an accelerating body, and the resulting F + F_i = 0 does look, on its face, like the statement that no net force acts on an accelerating body. Kanarev's insistence that the inertial force is not simply interchangeable with the applied force, and that its magnitude is only cleanly measurable when resistance is absent, is a legitimate warning against sloppy free-body bookkeeping. His four-phase car example is clear and concrete, and the paper is refreshingly explicit about what it is claiming.

But the contradiction he sets out to resolve is not a contradiction. The d'Alembert force is defined as −ma; writing F + (−ma) = 0 is a restatement of Newton's second law, not a separate physical statement, and it says nothing about whether the body accelerates. The inertial force is not a force acting on the body in the same sense as the engine's thrust — it belongs to a different bookkeeping frame, and mixing it into the same sum with real interaction forces is exactly the error Kanarev then attributes to Newton. Nothing in the paper derives the central claim that the inertial force "automatically" reverses direction at the onset of uniform motion; it is asserted, illustrated with the car and the asteroid, and thereafter used. That asserted reversal is the load-bearing step of the whole paper.

The asteroid argument makes the difficulty visible. On the standard account, an asteroid in uniform motion has zero net force and continues indefinitely because that is what the first law says; Kanarev needs an unexplained memory of a past acceleration, stored in the body and reversed in sign, to keep it moving. This adds a mechanism where none is needed, and it does not say what happens to a body that was never accelerated by any identifiable event, nor how the stored force's magnitude is determined, nor why it does not decay.

The over-unity section is the paper's most serious problem. An unbalanced rotor experiences internal forces whose moment about the shaft axis, averaged over a full revolution, is zero; an overrunning clutch can transfer the positive part of a pulsating moment to a load, but it cannot create net energy, because the negative part of the cycle is absorbed by the drive and by the mounting rather than abolished. The reported table — 344 W in, 6131 W out, an "efficiency" of 1782 % — asserts a violation of energy conservation, one of the most exhaustively tested results in physics, and it does so on the basis of a single voltage-and-current reading against a nominal 6 kW output. The measurement of P(output) is not described at all: it is not stated whether it was measured into a real electrical load or inferred from the generator's rating, which is the single most important detail for assessing such a claim. Since the input reads a near-constant ~6.1 kW output regardless of input power, the figures behave more like a plate rating than a measurement. No independent replication is cited; the sole reference for the device is the inventor's own web page.

Finally, the closing extension of the new law to the rectilinear uniform motion of photons is stated without argument in the paper itself and simply referred out to Kanarev's books, so a reader cannot evaluate it here.

See also

• Philipp M Kanarev — the author
• Isaac Newton
• Energy