iSoul In the beginning is reality

Center of vass

The vass is to time (duration) as the mass is to space (distance). As noted before here, the vass can be measured by a similar procedure as the mass. The mass and vass are inverses with opposite uses.

center of mass

The center of mass is the point that two or more particles (point masses) are balanced (or one large mass is balanced). For two particle masses, m1 and m2 that are located at points x1 and x2, respectively:

Center of Mass (CM) = (m1x1 + m2x2)/(m1 + m2),

which is the weighted arithmetic mean with the masses as the weights. This is similar to the momentum, in which the velocity is weighted by the mass: mv.

The center of vass is the point in time that two or more particle vasses are balanced. For two particle vasses, ℓ1 and ℓ2 that are located at points in time t1 and t2, respectively:

Center of Vass (CV) = (ℓ1t1 + ℓ2t2)/(ℓ1 + ℓ2) = ((t1/m1 + t2/m2)/(1/m1 + 1/m2)),

which is the weighted arithmetic mean with the vasses as the weights. Compare the celentum, in which the celerity is weighted by the vass: ℓu.

In order to generalize this, let’s use the derivation of the center of mass, as in Knudsen and Hjorth’s Elements of Newtonian Mechanics, chapter 9. Start with the time position vector, T, to find the center of vass for a system of particle vasses:

L Tcv = Σ ℓi ti,

where ℓi and ti are the vass and the time position vector of the ith particle vass, and L = Σ ℓi is the total vass of the system. Then differentiate with respect to space length to get

L Tcv´ = Σ ℓi ti´= Σ qi := Q,

where the total linear celentum of the system is denoted Q. In other words, the total linear celentum Q of a system of particle vasses is the same as that of a particle vass with vass L moving the the celerity of the center of vass. This is also stated as

Q = L ucv,

where ucv is the celerity of the center of vass.

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