Maks
Hi,

In last 46 years, until 196o (from 11. General Conference for Weights and Measures  CGPM) there is no solution for dilemma, are the supplementary SI units rad and sr base or derived units.

For solving this dilemma, here on this Forum, I will propose three new special base units, beside well known base unit for the length metre, which I think will clear the problem and help for better understanding of quantities and dimensional analysis too. (There is no need for physical quantity with mark 1 (one), or unit on minus one and also with no dimension). Dimension for angle, rad and sr, with this proposal are special base units too. Some formulas and equations will use r (radius) as part of the circle, instead rad (radian).

There are four base physical quantities plus Coulomb which are not connected with space:

1. Kilogram

2. Coulomb (not Ampere) ?

3. Second

4. Kelvin and

5. Mol

All others base or derived physical quantities depends of the choice of space shape: flat space or curved space (radius, revolution or cycle) .

Definitions:

Definition for the base unit length - metre is with dimension of time second

Definition for the base unit of time - second is with number of cycles

There is dimension (definition) for cycles with second [Hertz = 1/s ]???.

Flat space

Quantity..................Length...........L................metre...........................m

New proposal

Curved space  special base SI units for mechanics of circle and space and also for wave mechanics

Quantity................Circle.............Lo..............revolution......................rev
Quantity.................Period...........Lc..............cycle.............................cyc
.
Radius ( r ), revolution (rev) and cycle (cyc) are like golden units. They are universal and independent units. These units connect macro and micro cosmos and also flat, curved and fractal space. Everybody now what they are. They are like postulates. Dimensions as 5 r/s, or 5 rev/s are universal and we can calculate equations or formulas with them on the atom level and also on the planet level. Revolution and cycle are in use but with no definition like units (radius is new logical unit instead radian). Examples: rev/min, cyc/sec, Hertz, Amperetheard, rad/sec, and so on.

SI Derived units

Remark: lam=lambda, fr=omega

Length of circle..................O=2pR...........O= L/Lo............meter per revolution............m/rev
Length of period.................lam...............lam=L/Lc...........meter per cycle...................m/cyc
Wave circ. number.............No................No= Lo/L..........revolution per metre.................rev/m
Wave period number..........Nc(Rydberg)..Nc = Lc/L..........cycle per metre...............cyc/m
Circular frequency...............fo.................fo=v/O............revolution per second............m/s / m/rev=rev/s
Cyclic frequency fc (Hertz)...fc.................fc=v/lam.........cycle per second.............m/s / m/cyc = cyc/s
Speed/Velocity....................v.................v=L/T..............meter per second.............m/s
Radial velocity.....................vr................vr=R fr..............meter per second..............m/r r/s = m/s
Circular velocity..................vo................vo=O fo............meter per second.............m/rev rev/s = m/s
Cyclic velocity....................vc=c............vc=lam*fc.........meter per second..............m/cyc cyc/s = m/s
2p number..........................2pi...............2pi = O/R..........radius per revolution...........r/rev
Circular acceleration............ao................ao=v fo............meter rev. per sq. meter................m/s rev/s
Cyclic acceleration..............ac................ac=v fc.............meter cyc. per sq. meter................m/s cyc/s
Plancks constant.................h( ho)..........ho=mvO...........kg sq. meter per sec. rev...................kg m/s m/rev
Dirac constant...............h with tire (hr).....hr=mvR...........kg sq. meter per sec. rad...................kg m/s m/r
Cyclic constant ?...................hc...............hc=mvfr.............kg sq. meter per sec. cyc...................kg m/s m/cyc
De Broglie proposal...............h (ho)..........ho=mvfr............kg sq. meter per sec. cyc...................kg m/s....m/cyc ???
Newton radius force...............Fr=m ar.......Fr= m v fr.........kg meter rad. per sq. sec...................kg m/s r/s
Newton revol. force...............Fo=m ao......Fo = m v fo........kg meter rev. per sq. sec...................kg m/s rev/s
Newton cycl. force.................Fc=m ac.......Fc = m v fc........kg meter cyc. per sq. sec..................kg m/s cyc/s
Energy radius......................Er=Fr R.........Er = m v fr R......kg sq. meter per sec2.................kg m2/s2 = J
Energy revol........................Eo=Fo O........Eo = m v fo O....kg sq. meter per sec2.................kg m2/s2 = J
Energy cycle........................Ec=Fc lam.....Ec = m v fc lam...kg sq. meter per sec2.................kg m2/s2 = J
Bohr magneton.....................mi................mi = e v R /2......Coulomb sq. meter per sec. rad.......C m/s m/r
Current revolution.................Io=Q fo.........Io=C fo..............Coulomb rev. per sec...................Ao = C rev/s
Current cycle.......................Ic = Q fc.......Ic=C fc..............Coulomb cyc. per sec...................Ac = C cyc/s

and so on

With this proposal for new special SI base units, for example, there is a problem with dimensions and units in well-known equation for the photon quantum energy.

E = ho fc = ho c / lam

Dimensional analysis

h = ho = m v O [kg m/s m/rev]

fc = c / lam [m/s / m/cyc = cyc/s]

E = ho fc [kg m/s m/rev cyc/s] = [kg m2/s2 cyc/rev] = [J cyc/rev]

E = mf c2 [kg m2/s2] = [J]

So there is no way to connect this two different marks or different fields, mechanics of the circle and wave mechanics, in formula E = ho fc, without adding new parameter which connect them as n = cyc/rev. Such parameters also exist between cyc/r and r/rev (2pi ).

De Broglie has made such proposal with his wave theory, which claim that number of cycles in path of the electron must be integer. This was made with formulas and descriptive method not whit units.

lam = ho / mv and lam = 2p R/n =O/n

n = O/lam = [m/rev / m/cyc] =[cyc/rev]

Such test can be made for many other formulas and equations with use of new SI special base units.

06.06.2006

Maks
Abeer
but i don't understand how to convert the velocity from rev per second to meter per second...let's say 1 rev per second is how much in meter per second??
Maks
Hi Abeer,

Sorry I was late with my replay (summer time).

fo [rev/s].... [revolution per second]
omega = fr [r/s]. [radius per second]
fc [cyc/s]..... [cycles per second]
O [m/rev]..............[metre per revolution]
Lam [m/cyc]... [metre per cycle]
v = fo O [rev/s * m/rev]=[m/s]
v = fr R [r/s * m/r]=[m/s]
v= fc Lam [cyc/s * m/cyc]=[m/s]

For second part of your question the answer is that 1 rev per second is 1 rev per second. To get how much meter per second is 1 rev per second first you must choose dimension of the circumference O [m/rev] or radius R [m/r].

For example:
fo = 1 [rev/s] .[revolution per second]
R = 1 [m/r] or maybe R = 1000 [m/r].... [metre per radius]
O = 2pi*R=2pi*1=2p[m/rev]=6,28[m/rev]
O = 2pi*R=2pi*1000=2000pi[m/rev]=6280[m/rev]
Dimensional analysis;
2pi=O/R [m/rev //m/r]=[r/rev]
O=2pi*R=[r/rev*m/r]=[m/rev]
v = fo O=1*6,28 = 6,28[m/s]
v = fo O=1*6280 = 6280[m/s]

Maks

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