 Physics

# Defining Momentum Dean L. Sinclair's image for:
"Defining Momentum"
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Image by: The defining equation of momentum is p=mv. This little equation can be considered in two ways mathematically. It is the summation of all the forces which have acted upon the object in question from the first instant whenever that was. In calculus it is the integral of Force equals mass times acceleration over all time, from zero to the present. It is also possible to consider it as the instantaneous rate of something that is of the change of velocity if mass is a constant and simultaneously the change of mass when velocity is held constant. The integration of these two expressions gives two energy equations, the familiar, KE=1/2 mv^2 and done the other way, an unfamiliar "Energy," E=1/2vm^2. The summation of these two expressions would be the total energy of the body at any given time.

Differentiation of either of the two equations above, reverts us to the mv=p equation which we usually associate with linear momentum. If we differentiate another energy equation, E=hu relating the energy of a radiation to the frequency, "u," we get another equation which can be assumed to be a "momentum." This is "p"=h. Planck's constant, 6.63 x 10^-27 erg-sec. is symbolized by "h." If we assume that these two momentums will be equal with respect to a given unit under some condition we can equate the two to have "mv=h," or mv=6.63 x 10^-27 erg. sec. If we evaluate this at the speed of light, "c" and divide out "c" as 3 x 10^10 cm. We get an interesting little equation, "m"=2.21x10^-37 gram.cm. A moments reflection shows that this can only be true if we are talking about rotational motion wherein what we have called here, "m," is actually a torque of a mass of 2.21x10^-37 g. acting at a torque arm of one centimeter, or of a mass of 1 g. acting through a distance of 2.21x10^-37 cm.
Our reference body that we have here defined could possibly be a pulsating sphere varying, presumably at a net speed of light, between the two extremes noted, or possibly a pulsating ovoid with major and minor axes of the dimensions above.

What we are noting is that there seems to be an angular momentum constant to our universe, which,when evaluated at the speed of light, turns out to be a torque of (to three significant figures) 2.2lx10^-37 g.cm.

It can be noted that when the "mass" of a particle is inserted into the above equation, written in the form, mr=2.21x10^-37, "r," the torque arm, turns out to have the value of the "Compton Wave Length" of the particle. This is a value used in Quantum Mechanics. Apparently we have happened upon a connection between more conventional physics and Quantum Mechanics.

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