Capiert

The (Earth's) free_fall gravitational_acceleration at the Earth's surface (radius r1=6378135*[m], equatorial sea_level), is (ruffly (approximated (by me) to), simply) g1=~π^2*[m/(s^2)]-ac1 where π^2~9.8 is multiplied by the (proportionality constant of) units [m/(s^2)] (& then) minus its (=the_Earth's) centrifugal_acceleration -ac1=(vc1^2)/r1, with circumferential_speed vc1=cir/T=2*π*r1/T for a sidereal_day period T=23*[hr]+56*[min]+4*[s], T=23*[hr]*60*[min/hr]*60*[s/min]+56*[min]*60*[s/min]+4*[s], T=82800*[s]+3360*[s]+4*[s] T=86164*[s] & barely produces (a meager loss (from π^2~9.8), of e.g.) -0.34% at the equator. Hovering at higher altitudes have more centrifugal_acceleration. For any (other) height h=r2-r1 above r1 (sea_level, equatorial) the (larger) radius r2=r1+h is useful. g2=(π^2)*[m/(s^2)]-ac2, ac2=4*(π^2)*r2/(T^2) g2=(π^2) [m/(s^2)]-(4*(π^2))*r2/(T^2)), bring out π^2 & move the units into the brackets to (only) factor "1" g2=(π^2)*(1 [m/(s^2)]-(4*r2/(T^2))) is too complicated but assumes 4*r2/(T^2)=1 for a hovering, e.g. geo_stationary_orbit GSO (weightlessness), or g2=(π^2)*(1 [m/(s^2)]-r2*((2/T)^2)), let r2=r1+h & g2=gh g2=(π^2)*(1*[m/(s^2)]-(r1+h)*((2/T)^2)) <---! That (g2=g_h) is the free_fall acceleration wrt height h when using the sidereal_day period T=86164*[s] (which is a constant for any height h) & e.g. the Earth's polar radius r1=6,378,137*[m]. Examples: Equatorially: If the height h=0 at the Earth's equatorial radius (surface) r1=6399592*[m] then (the term) -(6399592*[m]+h)/(1856058724*[s^2])=-0.00344(646144442) which is ~-0.34(46)% (equatorial) loss from π^2*[m/(s^2)]. Try again, for GSO radius r2. g2=(π^2)*[m/(s^2)]-(4*(π^2)*r2/(T^2)), +(4*(π^2)*r2/(T^2)) g2+(4*(π^2)*r2/(T^2))=(π^2)*[m/(s^2)], let g2=0 for a GSOrbit 4*(π^2)*r2/(T^2))=(π^2)*[m/(s^2)], *(T^2)/(4*(π^2)) r2=(T^2/4)*[m/(s^2)], T=86164*[s], r2=((86164*[s])^2)/4)*[m/(s^2)], [s^2]/[s^2]=1/1=1 r2=(7,424,234,896)*[m])/4, r2=1,856,058,724*[m] is the Earth's GSO radius.

If I were to convert Electricity into average_momentum e.g. & average_forces, then this is how I would (mathematically) proportion (it, algebraically). To deflect its needle, a D’Arsenval meter’s average (e.g. steady state) electromagnetic_force Fai=I*(R^0.5)*Ki, I=V/R & 1/R=1/(R^0.5)*(R^0.5) is proportional to the current I & rooted_resistance R^0.5 & the proportionality constant Ki=Fai/(Pe^0.5)=1*[N/(A*(Ω^0.5)] which is 1*[Newton/(Ampere*rooted_ohm)] (&) that (can be determined by) the average electromagnetic_force Fai divided by the rooted electrical_power Pe^0.5=Piv^0.5=(I*V)^0.5 . That current’s electromagnetic force Fai=Fav is the same as the voltage's V=I*R (conversion from current I using the proportionality_constant R=Resistance, has the same) average electromagnetic_force Fav=V*Ki/(R^0.5), Kv=1/Ki=1*[V*(Ω^0.5)/N] Fav=V/((R^0.5)*Kv). Either (voltage or current) average electromagnetic_forces (Fai=Fav, are equal) Fai=(Pe^0.5)*Ki Fav=(Pe^0.5)*Ki & is proportional to the rooted electrical_power Pe^0.5=(I*V)^0.5 & (multiplied by) the proportionality constant Ki=Fai/(Pe^0.5)=1*[N/(A*(Ω^0.5)]. Electricity’s average (random=)heating force Fah=(Pe^0.5)*Ki is also proportional to the rooted electrical_power Pe^0.5=(I*V)^0.5 & the proportionality constant Ki=Fai/(Pe^0.5)=1*[N/(A*(Ω^0.5)], as (a random (scattering of the (repeated))) recoil, (Newton’s 3rd law opposite & equal) force (equivalent). Together both the electromagnetic_force Fai & the random heating_force Fah amounts are equivalent to an (arbitrary) average_force Fa=Fai=Fah & (are “multiplied” together to) make up the total electrical_power Pe=Fai*Fah/(Ki^2), where the inverse squared proportionality_constant is (Ki^2)=1*[(N^2/((A^2)*Ω)]. So, the electrical_power Pe=(Fa/Ki)^2 is a squared average Force Fa^2 per squared proportionality_constant Ki^2. What does all that mean? That means the average_force Fa=moma/t is equivalent to an mechanical average_force. --- (Please note: James Watt’s mechanical Power P=Pm definition Pa=Fa*va is an (algebraic) “average”_Power Pa using an “average” (steady_state) Force Fa=m*va/t of mass m multiplied by average linear_acceleration aa=va/t (my aa2 2nd order of motion); & an average_speed va=d/t of distance d per time t. My “electrical” average_Power formula Pe=Fai*Fah/(Ki^2) Pe#Pm looks very different from James Watt’s “mechanical” average_Power Pm=Pa=Fa*va. James’ (average) mechanical_Power is an (average_)Force Fa multiplied by a(n average)_speed Va; while my (average) electrical_Power is basically a “squared” (average_)Force Fa but divided by a squared constant. E.g. A(n average_)speed is (definitely) NOT a(n average_)force! Disclaimer: 1. But that is the ONLY way I know how to do it (=the conversion formulas), yet. 2. ..(because).. That is what the math & its (observed) proportions tells me. ) --- & that (average_Force Fa) is the rate of the average_momentum moma=m*va per time t; where the average_speed va=d/t is the distance d per time t, for a mass m. & that (average_Force) Fa=Fai is equal to the current’s average electromagnetic_force Fai. & if you know the average force Fa=Fah then you also (already) know the average (random=)heating_force Fah & the average electromagnetic_force Fai=Fav for either the current (thru a Resistor, Resistance) Fa=Fai or for voltage (thru a Resistor, Resistance) Fa=Fav or both (I*V) when rooted. Note: The units for the proportionality constant Ki=ki*[N*s/C] work out to be a(n average_)momentum [N*s] per Coulomb [C], e.g. [N*s/C]=[kg*m/(s*C)]=[(kg/C)*(m/s)] where a mass to charge ratio [kg/C] is obvious(ly), multiplied with an average_speed [m/s]. E.g.1 Let be given the voltage V=1*[V] the current I=1*[A] the Resistance R=1*[Ω] the rooted_Resistance R^0.5=1*[Ω^0.5] the electrical_power Pe=I*V=1*[A]*1*[V]=1*[A*V]=1 [electrical_Watt] the rooted electrical_power Pe^0.5=Piv^0.5=(I*V)^0.5=(1*[A]*1*[V])^0.5=1*[A*V]^0.5 . The average electromagnetic_force is Fai=I*(R^0.5)*Ki=1*[A]*((1*[Ω])^0.5)*1*[N/(A*(Ω^0.5)]=1*[N]. The average heating_force is (also) Fah=I*(R^0.5)*Ki=1*[A]*((1*[Ω])^0.5)*1*[N/(A*(Ω^0.5)]=1*[N]. That (easy example) doesN’T tell much, so let’s try something else. E.g.2 Let be given the voltage V=100*[V] the current I=5*[A] the Resistance R=V/I=100*[V]/(5*[A])=20*[Ω] the rooted_Resistance R^0.5=(V/I)^0.5=(100*[V]/(5*[A]))^0,5=(20*[Ω])^0.5=~4.7*[Ω^0.5] the electrical_power Pe=I*V=5*[A]*100*[V]=500*[A*V]=500 [electrical_Watt] the rooted electrical_power Pe^0.5=Piv^05=(I*V)^0.5=(5*[A]*100*[V])^0.5=(500*[A*V])^0.5=22.4*([A*V]^0.5). The average electromagnetic_force is Fai=I*(R^0.5)*Ki=5*[A]*((4.7*[Ω])^0.5)*1*[N/(A*(Ω^0.5)]=22.4*[N]. The average heating_force is (also) Fah=I*(R^0.5)*Ki=5*[A]*((4.7*[Ω])^0.5)*1*[N/(A*(Ω^0.5)]=22.4*[N]. Or else simply let Fa=Fai=Fah Fa=(Pe^0.5)*Ki, Pe^0.5=Piv^0.5=(I*V)^0.5 Fa=((I*V)^0.5)*Ki. Such (average_momentum electrical heating) will deliver moma=Fah*t, let time t= 1*[second] moma=22.4*[N]*1*[s] moma=22.4*[N*s] in 1 second (of time). In other words, the 500*[W] electrical (power’s) average heating_force Fah=22.4*[N] will deliver 22.4*[N*s] of average_momentum (heat) per second. 1000*[W] electrical will deliver 31.6*[N*s] per second; & 10*[kW] electrical will deliver 100*[N*s] per second.

Some people “boldly” say: 1 degree is 60 minutes (& DON’T think much about it). But I find 4 minutes is better & would have been more reasonable to make more sense, considering that shortcut used for ship navigation in the midevil ages. An Earth’s (solar) day is a complete revolution (cycle, (e.g.) angle wrt the sun), in 24 hours (time). (Note: Unfortunately (now) I find that definition of a day bound to both time & (cycle, e.g. 360°) angle. E.g. Instead of only time.) A cycle is 360° (angle). Wrt the sun the Earth’s angular_speed f=(angle/time)=1*[cycle]/(1*[solar_day] is the angle of 1*cycle=360°, per the time of 1*[solar_day]=24**60*[min/hr]*60*[sec/min]=86400*[sec]. So, (the proportionalities, are) f=360°/(86400*[sec])=0.0041667*[°/s], & inverted T=1/f=86400*[sec]/(360°)=240*[sec/°]. 240*[sec]*1*[min]/60*[sec]=4*[min]. T=4*[min/°]. That means we (on Earth) need 4 minutes per degree (turned). The Earth turns 1 degree (arc angle) in 4 minutes (time). So the Earth will turn 0.25° in 1 minute. 1 minute is 60 seconds 1*[minutes]=60*[seconds]. Time is time, & that conversion relation has NOT changed. The Earth turns 1/4 degree in 60 seconds f=0.25°/60*[sec]=0.0041667*[°/s] is still the same relation. That (4 “minutes” time) seems to be the only discrepancy with arc_angles' “minutes”; which (NOT to mention) also causes a discrepancy with arc_angle “seconds” due to the factor 60 (“times”). Does it (=the wording) get any more bizzare? I mean, do things right the 1st time & then you WON’T have to correct them later. Summarize: The Earth’s 1 day rotation (angle), has 360° (angle). 24 hours has 86400*[seconds] (time). It is obvious to conclude that 1*[minute]=60*[seconds] time of (the) Earth(’s) rotation, will sweep ¼ degree (arc of) angle. Disclaimer: Why then should there be 60*[minutes] (angle) in a degree (angle) when minutes were already defined for time? Why confuse things? A mistake is a mistake, please admit it; instead of (trying to) ice a poor cake (flop, better). & then somebody came around & tried to turn everything upside down because they (whoever started the mess) could NOT do the math correctly (originally). Continuity is demanded (=needed, for (fast, streamline) conversions); NOT a (complicated) half_hearted(=assed) attempt. (Again, why then should there be 60*[minutes] in a degree (angle), (when) that (unit: minute) already exists (as a time definition)? E.g. When minutes were already defined for time (only); & then somebody came around & tried to turn everything upside down (to fix it) because they (before (them)) could NOT do the math correctly (originally). (It's built on a mess.) I ask where are we in a (=this) modern world? CAN’T we (at least) correct our ancestors mistakes? Or do we have to continue & push the sludge thru? But for what reason? Mistakes ONLY slow_down progress=advancement. Some things are NOT worth keeping.) Thus it seems a bit ridiculous to claim 1° is 60*[minutes] (of arc), since (it does NOT make sense (with time), &) at least then (&/or) there the correlation to (the Earth’s) time has been lost by the (fake) redefinition of the “minute” as angle instead of time (anymore). I mean, had the Earth’s math (angle_speed) analogy been (correctly) extrapolated (finer); then less confusion had arisen for a (fake) distinction between minutes: in time; versus angle. Time had remained time (instead of the need to distinguish time names (e.g. minutes & seconds) from angles); & a (natural, wrt Earthly) conversion (from time) to angle had been obviously performed from the (Earth’s) angle versus time f=360°/86400*[sec]=1/(240*[sec/°]); or the inverse proportionality as time versus angle which is ((like) Period, but in other units) T=1/f=86400*[sec]/(360°)=240*[sec/°]. I mean let’( u)s face it, it looks like an (obvious) error has happened by the over_simplified redefinition (of (arc_)angle into time “names”, e.g. such as minute=60_seconds); & its (errorful misnaming’s) cover_up (still) has NOT corrected that (time versus angle, math) mistake=ERROR! I mean, according to them (old midevil naming): 1*[hour] (angle) is suppose to be 360°/24*[hour]=15*[°/hr] =15*[degrees]. But who says that? Who calls an hour(_angle)? Everybody recognizes an hour as (ONLY) a unit of time. Who calls a day, 360°? Motivation: I just wanted to point out that NONSENSE (with a complaint); & (note) the cover_up behind it; & propose an improvement. E.g. Conservatives DON'T like changing anything without a reason. Take it or leave it. You can perpetuate the erroring (if you want, NOBODY is going to hinder brainless idiocy, are they?; or else clear it. It’s YOUR choice. We have a lot of (fishy) relics left over from the past. NOT all are useful. Cheers

And from that you extrapolate this into being a widespread problem. If you will? Yes. It seems possible to me. (But) I DON'T need your wrath (if it goes against too much). Please explain. I thought "per" (=divided by) is rather clear. Please explain. I am rather greatful to that author. Years ago, I hadN'T a clue what he meant. With this thread & your team's help it (finally) dawned on me what he (might have) meant. His style technique, inspired me to recognize that (so). (That's a lot of years in between.) I can thank him for the inspiration (if I could). It (Ambiguous (unit) syntax) was a problem for me no matter how you see it. I just put the clues together. & it is (now) solved for me. (I am content with the results.) Which is more than I can say before starting this thread. I now have a solution method to deal with that problem (for me). A work around. Thus the problem has vanished. You DON'T need it (the solution); but I do.

Ok, but didn't I do that with my constructs? E.g. number (It(=the following variable k) is only a number) k=K/[unit], symbol (represents a composite=mixture.) K=k*[unit], unit (is stripped of all numbers.) [unit]=K/k. Those equations made a connection to each other. You however want me to separate them from each other. But I think that is already done, because of the equals sign = & which side of the equation they are on. The (3) variables k, K & [unit] are all each alone (meaning "separate(d)"). That I avoid (really using) numbers by using variables (instead), has (at least) separated numbers (e.g. 1,2,3..) as NON_existent out from my syntax. Ok. Only a number e.g. 1. Only a unit, e.g. [kilogram] (it has NO number). Only a symbol, e.g. M. (Warning: But I now know the Mass's symbol is M=1*[kilogram] (because I have seen the necessity) & so that (awareness of mine) might interfere with your (intended) lesson (for me). E.g. I can NOT overcome my intelligence; NOR the lack of it.) Is there any difference between those 2 words? Any reason why i? No units is fine; but you lost me with i. Types? Strictly math "numbers" 1,2,3? each has its own name: one, two, three, .. E.g. Ordinal (name & sequence), cardinal (value), irrational, .. Or do you mean (physic's) constructs, made of a number with unit? No? Good. Then they are constructs? (e.g. small formulas.?). =Sequence (order). E.g. Similar to a computing (pointer, pointing) language. E.g. Names; NOT (number_)values! Yes. But there, .. they have no number value. Instead they designate (dictate) the sequence (order). Priority (order). Quantities without knowing what (kind) from "several" possibilities. Yes. Yes, that is a bit (more) awkward for us (normal=typical) humans. Why? Only 1 symbol, or minimal (& sequence advantages)? OK. But, I doubt that I have fullfilled what you asked concerning separation. & I took the liberty to eliminate the typos, if you don't mind (because they disturb=distract my thinking=concentration).

Proposal: Now to summarize; & also be able to use either small (or large case, Capital) letters for proportionality_constants (&/or their variables, e.g. &/or their constructs), we might need an alphabetical subscripted syntax (=symbology, symbols). E.g. Please let the Hooke’s_spring’s proportionality_constant k=nk*[uk] where n is its number value & is its [unit], both multiplied together. Their subscript k denotes that they belong to the proportionality(_constant) (construct). Hooke’s_Law‘s proportionality_constant(’s symbology: as variables including both numbers & units) could then look like k=nk*[uk]=nF*[N]/(-nx*[m]). & where units: [N]=[Newton] [m]=[meter]. Disclaimer: What a (complicated) mess; (that’s why I (would) prefer Capital_letter constructs (=formulas) & small letter number_value variables (to get around that (ambiguous_syntax) problem); but it should work right. Again, only the numbers(‘ variables) are k=K/[unit] f=F/[N] -x=-X/[m]. Thus, only the number_variable (for the spring’s proportionality_constant), is k=(F/[N])/(1/(-X/[m]), rearrange k=(F/(-X))*[m/N], <---That (whole) is (ONLY) a number(‘s value)!; although [units] are (also) present. k=(F/(-X))*[m/N], *[N/m] k*[N/m]=(F/(-X)), <---Those are hybrids=mixtures: of number(_variable)s; & [units]. & (that proportionality_constant now has the correct [units]=[N/m]), k*[N/m]=K, swap sides as mixture_hybrid K=k*[N/m]. As Swansont said NO numbers are needed to obtain the units. Give an example E.g. Temperature T /K 20 30 40 I saw it in only 1 book by 1 (specific) author (he did all his tables that way) & (I) thought it was very peculiar (& (I) tried to figure it out but could NOT back then) because NOBODY else did that; but from the style (it looked like) he was trying to do something very fundamental. He wrote his units with a slash before them (units) under the symbol. Thus, Name Symbol /Unit number 1 number 2 number 3. So I interpreted that (2_Liner) Symbol /Unit to (elegantly) mean =Symbol/Unit (if it were written on ONLY 1 line).

--- 1st Please let me try a different perspective. I have seen Physic’s tables where the units are stated as “per”. Meaning the concept e.g. mass m would be ONLY a NUMBER; (thus) making it (e.g. the mass m as “ONLY number”; instead of a "number*unit" hybrid mix(ture)) convenient for multiplying & dividing ONLY as NUMBERs in e.g. an Excel table (sheet). NOW, to reverse (=swap) syntax for my convenience (only), please let (me make) the(=my, large symbol) Mass (concept) M=m*[unit(s)] (as construct) be made of (ONLY) a pure number (small character) m, & multiplied by its units in (square brackets) [kg]=[kilogram]. Then the “number” (of) mass m=M/[units] is the whole Mass_concept M but divided by its units [kg]. That is VERY IMPORTANT, because it has separated the (composite=hybrid=composite) Mass_concept into its basic (2) parts (of (ONLY the)) number m versus units [kg]. In that form(at) (of (physic’s_)concept per (its) unit), we can strip ANY (physics) concept down into ONLY its NUMBER value; which is independent of ANY (awkward) (NON_Unifying=NON_mathematical; alphabetic, (instead of numerical), word (e.g. unit); thus dealing ONLY with MATH! (e.g. with NO other hassels!). Motivation: Why do I say all that blah blah blah? Because it (=the number_variable, without units) is genial to be so unique. I.e. It has (a lot of) math advantages. E.g. We are NOT restricted to dealing with ONLY complicated (hybrid, mixture) relations. Instead we have LESS to do, which CAN increase efficiency thus make things go faster & be (or at least seem) simpler & LESS complicated. So, where are we NOW? NOWHERE my friend. But we can use what already exists. & the results are astounding! For instead of the units being multiplied by the number values; they are instead “divided” by the number( value)s! & Thus as Sears & Alonso said=stated “NOT” multiplied! But NOBODY could tell me why; because (if=when viewed only from that ("per unit") perspective) everybody (else) has been doing the math WRONG! (=Same method.) (Otherwise NOT?) Th(os)e (Physic’s) answers are also suppose to be a NUMBER but “per” UNIT!; instead of just beside the NUMBER (value). Strange that Sears & Alonso could NOT have said more about those (per) units to speed up the (discovery) recogition process. Disclaimer: I personally did NOT expect that I would ever have gotten a solution (=reasonable, logical (explanation=) answer) to that problem; & I had (then, thus) thought I must brainwash myself; & ONLY memorize the method (technique), (always) with the fear (=concern) of forgetting how to do it=((the math) things) correctly, (if I had forgot) (eventually) mixing things up (again). That puzzle (=paradox) is NOW solved. (So let's give it a whirl.) Please let Hooke’s (compressed_spring force) law F=k*(-x) be rewritten in Capital letters F=K*(-X). & Retry: (using (Capital letter) constructs for: ((small letter) “number”_)variables; & “units”). Please let the Hooke’s Law’s proportionality_constant K=F/(-X) be for the (math) constructs (=formulas, (that) I created in Capital letters). E.g. Please let the proportionality_constant K=k*[units] the (spring’s) force F=f*[N] & the displacement distance -X=-x*[m] which are also ONLY the number(_value_variable)s k=K/[unit] f=F/[N] -x=-X/[m] because the (Capital_letter) constructs (made of “number” multiplied by “unit”) are (then) divided by their unit (thus leaving ONLY their number(_value)). So again, the Hooke’s law’s proportionality_constant, (when) including units, is k*[unit]=f*[N]/(-x*[m]). We can ignore the (small_letter) number_variables thus leaving the (derived) unit k*[unit]=f*[N]/(-x*[m]). This_time (=That_instance, or example, had) NO ERROR occurred when deriving the (proportionality_)constant’s [units]; because it is algebraically sound=fit with (NON_ambiguous) consistent_syntax. I.e. NO ambiguous, double_meaning symbols. The (3) math constructs eliminated the inconsistent syntax.

Thank you for the help. Good that you noticed. But my wrong answer was a typo. Then (it=proportionality is about), estimating? That math has always turned my head (crazy). Agreeable. Also fitting. It all seems to make sense. Studiot, I am sorry (disappointed) I typed the wrong answer for you. I had tried, but I made a (stupid) decimal ERROR. I had it right in Excel but I copied it wrong. (Too many problems with my eyes.) m=D*vol=44.444.. [g/L]*0.175 [L]=7.777.. [g] [NOT 0.777]. Considering, that mistake had NOT happened, why (then) should I do otherwise (& estimate) when it is so simple (& exact)? I mean, I assume, I still would have (probably) made the same (or similar) mistake. (Blurry vision, +.. . Reading glasses are NOT going to help that. Nor had the optometrist's cortisone brought permanent success.) We is we naive (NON_physicists) who have NOT a clue (what is happening). Abracadabra. Sometimes it is & then sometimes it is NOT. There you go. "Now" you begin constructing. Although they are NOT visible before (hand). That is all fine Swantsont. But a fundamental step is missing (which you obviously miss(ed)). Quite right. I told you in advance. As my problem, I consider then that I should solve it, with constructs.

Then I have a Density D=m/vol=10 [g]/0.225 [L]=1 [g]/0.0225 [L] (wrt a simple mass of 1 [g]); or else) D=44.444.. [g/L]. That is where the Density's units (suddenly) pop up. Only by using a specific (numbers) example can we (suddenly) see the units. It (=That pop_up, inclusion) goes (=happens) effortlessly. (It's (easy (&)) automatic.) But I typically do NOT use numbers algebraically, because irrational_numbers are very messy. I usually deal with (general) variables (for (very loosely speaking:) "any" number), & (=but) typically only use (exact) values (rarely) when I need some form of extra orientation. The disturbing part for me here in Physics is the inconsistent syntax (& or method?); which causes me to runamuck. I would prefer all symbols had (also) their units (multiplied) with them to be (obvious &) consistent; but you (Physicists) DON'T deliver that (consistency) because it looks messy. ((&) It's (also) NO fun!) & then peculiar problems (occasionally) start to happen that I can NOT (always) explain or else I have difficulty explaining (because they are so rare, & foreign). If my Density is D=m/vol, swap sides m/vol=D, *vol m=D*vol. My new mass (would be) m=D*vol=44.444.. [g/L]*0.175 [L]=0.777.. [g] How can you find (=derive) the (proportionality_constant's) units without number( value)s? Answer: NOT known. My problem is here at D=m/vol; there is NO Problem after the 2nd "=" at "10 [g]/0.225 [L]". There is something missing for me before the 2nd "=". Maybe I also need a (fake, (temporary) dummy, placeholder) unit's_variable symbol too? (for (premature) consistency) e.g. Density, is D*[units]=m*[g]/(vol*[L]. ? But it clashes in my head brutally. Thus Failure.

Thanks for your attempt to try & understand "my" problem. (It helps me try to look at it closer.) But I think you missed it. My problem is the clash between inconsistent syntax. I.e. 2 different syntaxes=formats. (They (DON'T) mix like oil & water.) (It's a MASTER & SLAVE relation.) (BEFORE derivation:) Both F & x have units; BUT k does NOT. Thus k's units "must" be "derived" from them. That is a 2 step process instead of ONLY 1 step. (I recover=repair it.) k's units do NOT exist then (before that) until they are derived. (& it is a tricky 1_way street, until done!) Attempting to (algebraically) manipulate F's & x's "units" before that (derivation, for k's_units (obviously?)) will fail. That's the catch, the whole problem. Maybe my thread's title should have been named "(Proportionality_Constant's) Units ((perplexing), derivation)?" instead. Or something like that?

Absolute(ly). The cancelation (of units) is NOT my problem. My (automatic) inversion of the units is my (internal) problem.

My (major) problem (obstacle) is intuitively (a) psychological (block(age)) when using the 2 (thus) inconsistent ((conflicting(?) syntax) methods (at the same time?) while dealing with the units (derivation). Please let me explain what I observe (mathematically). I estimate I automatically get the algebra (answer) wrong with (a fake) ~40%. That is I (repeatedly) make the same mistake; but recognize it (just in time), to correct it (so that (in the end) it does NOT seem like I am making a mistake (at all); although I really do ERROR!). I find that very peculiar, why I can NOT directly proceed to the correct answer; but instead I must always make the ERROR 1st; & then go thru the routine of correcting it 2nd. That is a waste of time; & a risky proceedure (e.g. if severely distracted). But, what is happening in my mind does NOT make SENSE unless there is a reason for all that (NONSENSE, detour). I must conclude that the k=F/(-x) construct is EITHER a ruff forced_fit which does NOT (naturally) belong (together); or else there must be another explanation (which I (might) have missed)? What I see is, units are typically NOT included for the symbols F & -x (but) until the number( value)s are stated (=declared). However, k does NOT have any (units, at all before that); thus those units are NOT known; but still (NO_units means they) must be found ..from somewhere! Strictly speaking, for me, I have 2 alternatives: e.g. either to borrow them (units) from F & -x by cross_multiplying them to k; but then they are (wrongly) inverted; & so I correct that inversion; & notice that I have only copied those units from F/(-x) in(to) the same positions. I DON'T (think I) have to say how little mathematical SENSE that makes (to me), with a 1_sided abracadabra copy (of units), from F/(-x) to the (empty=NO_units) k side. It is simply a (functional) fix=repair just to make things work without explaining why (things fail, or why they should work, but do NOT, without that trick (of the trade).) Disclaimer: EVERYBODY KNOWS how to make the units (derivation, work correctly; by repairing=correcting it); BUT NOBODY tells (me) why (that trick is NEEDED (at all); other than that it is NEEDED). My mind deals with that problem like a paradox (conflict); & WANTS to shut (it) off like a clap TRAP. It is like asking (for) a yes or NO answer but the priority (dominates, &) immediately locks up (=latches) into the NO priority, as stolen! It's VERY sticky gumming up my thinking process(es). ONLY a "corrected" wrong_answer will function correctly.

I was always stunned by the complexity. Proportionality constants exist (almost) everywhere (in Physics), & their complexity has always stunned me; but (peculiarly) I have NOT seen (a textbook) anywhere on how to make (=derive) them (as though (derivation (of their units) is) avoided); so I thought I would give it a whirl (=try) (on my own, as DIM =Do it myself). (It’s only common sense. Dealt with intuitively, due to the(=my) confusion.) Recap: 1 of the most basic (& yet easy (but tricky)) concepts (rarely found in text books) is deriving (=how to derive (them)) proportionality_constant’s “units”. --- Disclaimer1: (I suspect) E.g. Maybe (perhaps (because)) from the (misleeding?=confusing, conflicting) contraproductive (brainwashing) statement(s) (e.g. from Sears; & Alonso): that units are NOT (suppose to be) multiplied by the symbol’s number (value(s)), (but) when they (perhaps) really are (multiplied), instead; but few (people=physicists (have)) admit(ted) it. (Even) although NOT perfectly ((multiplied) sometimes) due to singular versus plural (units, syntax). Maybe some people get the basic idea right=correct. Math is suppose to be an exact science (sometimes). Units are (typically) NOT included into formulas until the number values are (present(ed)). ((Rule 1: (Simply) include the units; Rule2: & then copy them (units) to the constant. Rule3: But how?)) Note: I’( ha)ve used square_brackets for units, here. --- E.g. Hooke’s law (for) a spring. The proportionality k=F/(-x) (looks like a quotient=ratio, to me, &) is the Force F as main actor (influencer, cause); wrt the negative displacement distance -x as secondary actor=slave (result, effect) e.g. which is in the opposite (=negative) direction. (Simply) include the(ir) (multiply_)units; k*[N/m]=F*[N]/(-x*[m]) then “copy” (them, units) to the constant, for equality. Keeping in mind that a [Newton] is [N]=[kg*m/(s^2)] & Force is F*[?]=m*[kg]*a*[m/(s^2)] the unknown units for Force are (simply) [?]=[kg]*[m/(s^2)]=[N]. Applying the same method for Hooke's proportionality constant k*[N/m]=F*[kg*m/(s^2)]/(-x*[m]), cancel [m/m]=[1/1]=1 k*[kg/(s^2)]=F*[kg/(s^2)]/(-x), swap sides. The k constant’s (unique) units are [kg/(s^2)] kilogram per second(s)_squared, or [N/m] Newton(s) per meter. Again, take the ratio (=quotient) including (multiplied) units k [N/m]=F*[kg*m/(s^2)]/(-x*[m]), swap sides F*[kg*m/(s^2)]/(-x*[m])=k*[N/m], *(-x*[m]) F*[kg*m/(s^2)]=(-x*[m])*k*[N/m], rearrange F*[kg*m/(s^2)]=-k*[N/m]*(x*[m]), /[kg*m/(s^2)=N] remove(=divide_by) units F=-k*x, gives us the standard recognized formula (Hooke’s Spring Force). E.g. A (weight_)scale could displace its spring -1 [cm]=-0.01 [m] (down), per [kg]. That force (weight) Wt=m*g=1*[kg]*9.8*[m/(s^2)]=9.8*[kg*m/(s^2)] would be 9.8 [N] for 1 [kg] (mass). Using Hooke’s spring law(=formula) F=-k*x, swap sides -k*x =F, /(-x) the spring’s proportionality constant (e.g. ratio) is k=F/(-x), let the Force F=Wt weight Wt=m*g k=m*g/(-x), let the mass m=1 [kg] & the gravitational_acceleration g=-9.8 [m/(s^2)] k=-9.8*[kg*m/(s^2)]/(-0.01 [m]), 1/0.01=100 k=980*[kg*m/(s^2)]/[m]), cancel [m/m]=[1/1]=1 k=980*[kg/(s^2). That spring (law) formula F=-k*x, swap sides -k*x=F, /(-k) can be manipulated to find the displacement -x=F/k for (e.g. calibrating to) the mass m=Wt/g -x=m*g/k, *(-1) x=-m*g/k, let g=-9.8 [m/(s^2)] & k=-980*[kg/(s^2) x=-m*(-9.8 [m/(s^2)])/(-980*[kg/(s^2)), 9.8/980=0.01 & [(s^2)]/[(s^2)]=1/1=1 x=-m*0.01 [m/kg]. E.g. let mass m=1 [kg] x=-1 [kg]*0.01 [m/kg], [kg/kg]=1/1=1 x=0.01 [m]=1 [cm]. All pretty obvious. Disclaimer 2: Such a constant k (as ratio), also looks like it could serve (well) as a variable, instead (e.g. if needed, when a (so_called) constant is NOT constant, at all). If that'( i)s the way things are done(?); then it would be a help (to me).

Thanks Sensei. That's a good example. I will have to give it some thought (time). NO arguments there (with those Temperature Energy concepts commonly used). E.g. Those approximations work (often). (But I have to remind you that I am looking for an alternative (Newtonian math) concept; instead of (Leibniz's) Energy that will work just as well; if NOT better with fewer ERRORs.) (I envision) Temperature T=k*va/m is a quotient (proportional to) the particle's average_speed va "per" mass m (instead of "factor" "multiplied by" for the product of (average_)momentum moma=va*m); (&) where k is simply some sort of (correction) proportionality_constant. That is simply 2 different math methods: e.g. T (quotient) versus KEd (product); using 2 similar parameters: e.g. the average_speed va & which is then either: divided by or (else) multiplied by the mass m. 2 methods (alternatives) occur to my mind. E.g. I can convert existing energy values into some kind of momentum; or else (I can abandon that method completely) & concentrate on the average_momentum squared concept as a mass*Energy substitute. I will need too much time to (accurately) prepare that (details); & hinder errors (stumbling blocks). Please (excuse me, but) would you (please) prepare th(os)e Energy calculations (for me) & I would attempt to convert that (in)to (some kind of) momentum. I would then know what (numbers) to expect & whatever format you desire (if I wish to copy it). I consider I might be a better editor than author.

That (shockingly) seems like a noun (thing); but I got your drift, meaning concept. I think Swansont gave you (=us) your best (=simplest) so_called "crap" Energy example with a head on head collision of 2 masses each 1 [kg] at speed(s) v=(+/-)1 [m/s]. That'( i)s at sub_light speed(s); & the Energy does NOT agree with the momentum! (Need I say more?) E.g. Mass 1's mass m1=1 [kg] & (accelerated) speed_difference vd1=1 [m/s]; mass 2's mass m2=1 [kg] & (accelerated) speed_difference vd2=-1 [m/s]. Really? The average_momentum (of each mass) is moma1=m1*va1=1 [kg]*1 [m/s]=1 [N*s] moma2=m1*va2=1 [kg]*(-1) [m/s]=-1 [N*s] momat=moma1+moma2=1 [N*s]-1 [N*s]=0. The total (average_)momentum is zero! However, the(ir) kinetic_energy(differences) are each 0.5 [J]; so, their, total input (Energy) is 1 [J]; but their NON_elastic (collision) result is zero Joule. KEd1=m1*vd1*va1=1 [kg]*1 [m/s]*0.5 [m/s]=0.5 [J] KEd2=m2*vd2*va2=1 [kg]*(-1) [m/s]*(-0.5) [m/s]=0.5 [J] KEdt=KEd1+KEd2=0.5 [J]+0.5 [J]=1 [J] total kinetic_Energy(_difference) input but the KEd_output=0 because all speeds are (gone to) zero meaning -1 [J] lost, abracadabra! What a bunch of JUNK! When assuming the speed_difference vd=vf-vi; & each initial_speed is zero vi=vi1=vi2=0 then their speed_differences vd1=vf1-vi1=0-1=-1 [m/s], & vd2=vf2-vi2=0-(-1) [m/s]=1 [m/s]) (for masses 1 & 2, are); where their (linearly_accelerated) final_speeds vf1=vi1+vd1=va1-vd1/2 vf2=vi2+vd2=va2-vd2/2 are the initial_speed vi plus the speed_speed(_difference) vd; &/or vf1=va1-vd1/2 vf2=va2-vd2/2 the average_speed va minus half the(ir) (accelerated) speed_difference vd/2. That (sure) sounds like a false claim on your part. I'm quite sure the experiments (will) show the discrepancy (ERORR) between (average_)momentum versus (kinetic_)Energy(_difference) results. Kinetic_Energy is a looser & you guys are trying to cover up that (fact). E.g. With "dark" (=unknown) energy on a galactic scale. But I understand you (all) HAVEN'T a (faintest) CLUE because it is in your natural character to deny things you do NOT understand because of your education. Scientists can be typically the "LAST" person to learn what is new, because their education (brainwashing) interferes with what is obvious. (I.e. Common sense. Who has it? Every healthy person!). Typically, instead of saying they (scientists) have made a mistake; they (scientists, I DON'T want to mention any names) say, (=mildly admit) they (scientists) have discovered other than they ((have) wrongly) expected. WOAH! If the mistakes (=ERRORS) are NOT going to be admitted (& recognized); then how are "we" going to progress (e.g. in Physics) (& eliminate those errors). E.g. Recognition is the 1st step to improvement. By the look of it some of their study was in vain. They forgot something (very important) like (e.g.) the initial_speed vi=vf-vd (especially if that is light's_speed c) which they love to eliminate in their (linearly accelerated) speed_difference vd=vf-vi. I'm NOT telling you something NEW; (but instead) just reminding you. Your calculations are full of holes if you have forgotten missing (initial) terms (which are prove_able with simple algebra (math)). You (=your colleagues & predecessors) have built up an unreliable empire ready to crumble; if you rely on ONLY those incomplete equations (with missing terms) that you (so) carelessly ignore & (even) reject. Still a good tip, I'( a)m convinced. LaTex is (a spastic) over_kill because the programmers could NOT correctly convert all the(ir) .pdf or whatever formats. They did NOT know enough about the different text formats; so they invented their own (NON uni_directional) format to make things work (somewhat) correctly. Why the overhead (just because they could NOT do their task)? Now you are demanding everybody follow "their" mistake('s remedy). There exists (more than) a (=1) NEW text editor every (10) year(s). How many have I learned? & then NEVER need (it) again because something better comes (along), to overtake the situation; because the last (editor) was inferior. This 1 (LaTex) does NOT go backwards, e.g. it does NOT convert backwards into e.g. a Winword or .pdf file, because the programmers do NOT know how to do that (conversion) correctly (originally), so what have they learned? Here today, (but) gone tomorrow. Is that (programming), (called) science (Physics)? NO(! way (my friend)) that is NONSENSE, e.g. NOT understandable. You have peculiar "demands" because you CAN'T get your own act together. I'm only making (improvement) suggestions (to try & get out of the problems). You want to avoid your (existing) problems (& say they do NOT exist). E.g. Ohhh there are limitations! (..but because the formulas DON'T always work). Let us (both) say, there is room for improvements. It'( i)s NOT easy to change mainstream (opinions!). Einstein & Michelson both stood "against" mainstream; & look at where we are NOW. They (both) changed it (=mainstream) (instead of (completely) correcting it). What a mess! To summarize (this thread), I have made 2 suggestions: either: to kick_out (the scalar) Energy as NONSENSE; or else (if you want to keep Energy, although I do NOT know why) to vectorize it (=Energy) (as needed) (& eventually factor it (=Energy) with the scalar (called) mass (again) (as a distortion) mentioned in another thread: acceleration note) as an improvement. Disclaimer2: I do NOT find those (2) suggestions (either): rude; NOR (as) arrogant constrictions; but instead as liberal alternatives for improvement. E.g. You may choose either way; if you want to choose at all. I have only tried to state my observations & conclusions for that (part) of the development. Take it or leave it. Your past scientists did NOT like Galileo either; NOT to mention Ohm, Einstein, Michelson, Wilson (plate tectonics), ... You are all typically (mostly) of a rejecting attitude (tendency). It takes (much effort &) a very long time to convince you otherwise. But history repeats itself. For sure.

Most probably a (bio)chemical energy (reserve). I disagree, at STP solid CO2 is very cold & that temperature difference (while) melting can change pressure which can do work. Yes, but that is (chemical) bonding energy (exchange). Yes Sensei, (I agree, we have all those (Energy) concepts with their (own) math); but can't we use e.g. (average_)momentum; instead of Energy_math? Why "must" we use ONLY energy? I see more disadvantages with Energy; than advantages.

Ghideon, that is excellent. Exactly what I want to say.

I do NOT see anger in my statement, ONLY (resignment &) reassurement that Energy does NOT always add thus it is (in that sense) unaccountable ("NONSENSE!"). If things do add up as they are (expectedly) supposed to then they are behaving illogically. Denying the problem is NOT going to cure it. Unlike most (people) I am (at least) recognizing a problem & (then) attempting a solution. As long as that takes (me). It is NOT an easy task. Especially in only 1 shot. I disagree. I was only summarizing so you can recognize the direction. You have NOT addressed the major question. I.e. Title. That is NOT my question. Especially because I know Energy is an approximation & thus relative. I (already) know you guys (& gals) already use math_Energy for many things, because it compares. You are trying to change my question in order to avoid it.

Please let me help you. Inability to learn so (=such) simple things causes that your other posts to be unreliable. Are you sure you mean unreliable? How?

I agree with you Sensei. I am unable to learn LaTex & your programmers were unable convert text formats correctly. Thus they created a 1 directional conversion you call Latex. But I must say my post looks (a little) better than yours.

I tend to think, we do NOT need (kinetic_)Energy(_difference)’s (redundant) syntax. Let’( u)s face it. Energy is NONSENSE! E.g. 1 Astronomer’s have been complaining for a long time. Now(adays, or a_daze) you (also) have “dark” (=unknown) Energy to cover up that problem. E.g. 2 The output of a NON_elastic collision is always less than the input. I.e. NO matter how (much) you (want to) “guess” explaining its (NON_elastic) loss (e.g. with deformation (dents), acoustic noise (produced), & heat (warmed)); instead of knowing & measuring. Mathematically that loss is calculate_able (accountable, into a reduced_mass (construct)).) E.g. 3. That (NON_elastic collision, Energy loss) is NOT energy conservation but instead a math ERROR (caused by) incompatibility with (average_)momentum. But my question is, do we (really) need the Energy (math) construct, at all? I mean we already have (average_)momentum & it (=that (average_)momentum) does NOT seem to lie at us like Energy (sometimes) does. With the (kinetic_)Energy (construct) we “loose” information. I.e. It (=KEd=delta_KE) is NOT completely “reversible” math (without using the original( parameter)s again); which hinders a (bidirectional math) reverse_ability. E.g. (For linear_acceleration) the kinetic_Energy(_difference) KEd=m*v(d)*va is composed (=made) of: a (=1, single) scalar (mass m); & “2” (speed) vectors (the speed_difference vd=v(d)=v=vf-vi as final_speed vf minus initial_speed vi; & multiplied by the average_speed va=(vf+vi)/2=d/t as added final_speed vf & initial_speed vi divided by 2) . Th(os)e (2) speeds are vectors because they have “direction”, (also) meaning (each) in simplest form e.g. if in 1D, (the) travel can be either: positive (forward(s)); or (else) negative (backward). Mass (is a scalar, &) can NOT do that (bidirectionality). --- Disclaimer 1: I have NOT seen a “negative” mass -m (for that) coefficient (factor m); even if you rave about anti_matter; simply because it (=anti_matter) is (let us say) opposite_charge of (perhaps) a spin. The rule is, every charged (sub_atomic) particle, has its own oppositely charged (so_called aunty_) particle. (Does that include neutral (uncles)?) But during annihilation, at such a subatomic size, how can you prove your guess_work (=assumptions)? That (tracking) seems (to me) impossible to follow; & only a careless (misleading) idea. --- A vector (e.g. such as a(n average) speed v(a)) multiplied by a scalar (e.g. mass m) remains a vector (e.g. (average_)momentum mom(a)=m*v(a)) . But 2 (negative) vectors (e.g. speeds vd & va) loose their (negative) polarity -1=j^2 when multiplied together to become (& always stay, only) positive (scalar); (no matter) whether they were originally positive or negative. That is a loss of (the +/-) polarity information, which is NOT retrievable (=recoverable, salvageable) without using the (original) polarity (again). E.g. Using a factor *v/((v^2)^0.5), where the (linear_accelerated) speed_difference vd=v & visa versa (is the truncated_symbol syntax) v=vd, because they are identical. (I simply truncated the d.) The (vectorized) kinetic_energy(_difference) (e.g. as a) vector KEd=m*v*va*v/((v^2)^0.5) is the (scalar) KEd=m*v*va multiplied by its speed_difference’s polarity v/((v^2)^0.5). If that speed_difference v=vf-vi was negative then its KEd will also become negative. That is why I say (=question) do we really need (e.g. kinetic_)Energy? if we have to (re)modify so much; (because) it(s Energy_math alone) is inferior (NONSENSE). Why DON’T we (just) kick out the concept of Energy (all together)? & throw it away in(to) the garbage. Why do we perpetuate the error_making problems, (called) Energy? Why do we bother, at all, with (the concept, approximation) Energy? (E.g. I have proposed bending (=modifying) Newton’s motion laws (as detour) to get around the Energy error problems; (but that (detour) is) instead of dealing with the real (guilty) culprit (i.e. Energy).) It (=Energy) is way too complicated for what is needed. Energy (syntax, (an) approximation) was invented ((ruffly ~2*KE) by Leibniz; it’( i)s NOT Newtonian) to help describe linear_acceleration(’s work). But Leibniz originally confused mass m=Wt/g with weight Wt=m*g. It’( i)s the gravitational acceleration g=Wt/m that (had) caused that (confusion) problem for him (=Leibniz).

That's right! I'm only interested in the real McCoy. (E.g. Spare me the science fiction. I DON'T need Sc_Fi (like they do).) Thank you. Pity (for them).

But you can move thru time without moving thru space e.g. maintaining the same distances (so to speak). Special Relativity was retracted by Einstein as defect, but (it was) a means to an End=his General_Relativity. Ch 22, 1920. Meaning Special Relativity does NOT (always) work. So I guess you lost that 1 arguement. Meaning time can NOT be a dimension. Sorry (for you).

What (is that suppose to mean)? I did NOT say we can do without time. Time is something else (an extra) which is necessary, but it does NOT belong to (category) dimension. E.g. I am alive, I live & breath (air) eat (food) & drink (water). All those extras, but they are NOT me.

I see NO evidence of that. Please explain. ..because.. You have heard (=read) my version. E.g. Dimensions (x,y,z) are all at 90° to each other. (That (3 mixture) starts at x; & ENDS at z, the last (alphabetic) symbol (but chosen) on purpose, intentionally (to prevent further ones).) Time is NOT at 90° to ANYTHING! Time does NOT belong to the category "dimension". It (=Time) follows NO previous example, thus it is unique, a category of its own (nature). I see NOTHING else to prove & convince me otherwise. It (= That (time) nature (=behaviour)) is very obvious (to (at least) me). Disclaimer: I DON'T care how badly Minikowski distorted the description of time in the past; it (=his distortion) is NOT fitting. Time reversal is NOT possible.