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Momentum and energy play very similar roles in mechanics, each being changed by the application of force over a interval. For energy the interval is in space and for momentum it is in time. Both have associated conservation laws.

Yet, energy units are named in many systems and momentum units generally are not (and in particular are not named in SI).

Is there a clear historical reason for the difference?

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    $\begingroup$ I don't know where you go the impression that there is no SI unit for momentum. It's called the Mom, 1 Mom=1 kg.m/s. The milliMom is also known informally as the "Mommy," and the kiloMom as the "big Mama." $\endgroup$ – Ben Crowell Oct 22 '15 at 14:35
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    $\begingroup$ I can't tell if you're joking... :) $\endgroup$ – Ne Mo Oct 22 '15 at 16:33
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    $\begingroup$ @Ne Mo: Joking? Why would I be joking? Also, the megaMom is nicknamed the "mother of all momenta." Use of the microMom is discouraged, because it's so small -- it shouldn't be Mom until it grows up. $\endgroup$ – Ben Crowell Oct 23 '15 at 15:55
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There is a historical reason. But it was not a fluke of history, the underlying reason is that energy comes up in non-mechanical (thermal, electric) contexts whereas momentum does not. Derived alternative, newton-meter in SI, did not arise naturally in such contexts, and alternative units, like calories, were used prior to the discovery of the general energy conservation law. It made sense to replace them with named standardized units. Klein's Science of Measurement is a nice historical survey.

Standardization and naming of units happened in two waves. First started during the French revolution at the behest of Taleyrand (known as bishop turned politician who later managed to serve as foreign minister under both Napoleon and Bourbons after Waterloo). French Academy appointed a committee on weights and measures, including Condorcet, Lagrange, Laplace, Monge, and unofficially Lavoisier before he was guillotined, came up with the foundation of SI. At that point only the base units of length, time, weight and temperature received single names. The derived units of area, volume, speed, acceleration, work/energy, torque, momentum, etc., were combinations of the base ones even if they had commonly named units like liters or knots. Future kilogram, called kilograve, was the unit of weight, i.e. force, not mass. Mechanical energy and momentum received equal treatment.

The second wave, started in 1860s and formalized by 1880s in both SI and its competitor CGS, was meant to catch up with developments in thermodynamics and electromagnetism, and gave us ohms, volts, farads, watts, etc. Kilograve renamed into kilogram became the unit of mass, the unit of force was named dyne in CGS (from Greek dynamis - force), and newton in SI. What of energy? Its mechanical manifestation received no new attention, but in 1864 Clausius suggested erg (from Greek ergon - work) to replace calorie as a unit of thermal energy, a remnant of by then discredited caloric/phlogiston theory. It was adopted in CGS. The unit for power, watt, was suggested even before joule, by Siemens in 1882, to replace Watt's own horsepower used to measure output of steam engines. Siemens was an electric engineer. Joule himself was honored by a unit name for determining the mechanical equivalent of heat. Momentum was out of luck.

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In 1887 a committee of the British Association was appointed for the purpose of "considering the desirability of introducing uniform nomenclature for the fundamental units of mechanics of co-operating with other bodies engaged in similar work.” The committee issued a series of questions to members, and collected their replies. The result was that in 1888, when the committee met at Bath, they were able, amid much difference of opinion, to agree as to the desirability of introducing names for the C. G. S. units of velocity, momentum, and pressure; the names suggested being, kine, bole, and barad respectively.

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  • $\begingroup$ This is very interesting as some of my education was conducted in cgs units but even there no one mentioned a named unit for momentum. $\endgroup$ – dmckee Feb 16 '17 at 22:53
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    $\begingroup$ Somehow the proposed cgs units kine and bole were not very succesful. In 1891 the electrical engineer and inventor William Henry Preece said "They tried to thrust upon us the term barad as indicative of the standard of pressure, bole the unit of momentum, and kine the unit of velocity, but I think this attempt has practically failed, and I have met but one case where one of these names was used." By the way, bole might be derived from a Greek word meaning throw, as in hyperbole and parabole. $\endgroup$ – jkien Feb 19 '17 at 22:27

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