Hyphenating complex physical units

I have been reading about writing conventions for scholarly articles recently - specifically, physics - and have learned that when writing units, write them out if they are not associated with a numeric value ("how many meters....?" rather than "it is 5 m long").

But what about more complicated units? Take momentum, which is kg⋅m/s. Do I write "Momentum has units of kilogram-meters per second" or "Momentum has units of kilogram meters per second"?

Wikipedia seems to accept both but prefers no hyphen. Can someone give me a reference which actually states a preference of one over the other?

Solution 1:

As the comment above notes, the SI brochure states:

In both English and in French, when the name of a derived unit is formed from the names of individual units by multiplication, then either a space or a hyphen is used to separate the names of the individual units.

In Section 7.80, "Hyphens and readability," the Chicago Manual of Style advises (emphasis mine):

A hyphen can make for easier reading by showing structure and, often, pronunciation. Words that might otherwise be misread, such as re-creation or co-op, should be hyphenated. Hyphens can also eliminate ambiguity.

On pg. 14, the AIP Style Guide echoes the advice of the Chicago Manual:

Modifiers made up of two or more words are usually hyphenated. When such hyphens forestall ambiguity, they are essential.

The salient quantity in kilogram meter per second is the kilogram-meter; after all, what's being measured is not the meter per second (velocity) or the kilogram per second (my weight gain on weekends), but the kilogram-meter per second.

So to highlight the composite term formed by multiplication, I (and this source) would write:

The kilogram-meter per second (kg · m/s or kg · m · s -1 ) is the standard unit of momentum. Reduced to base units in the International System of Units (SI), a kilogram-meter per second is the equivalent of a newton-second (N · s), which is the SI unit of impulse.