This question isn't just about kilogram-meters, it's about multiplied units in general.
I have a good mental conception of divided units, e.g. meters per second or grams per cubic meter. Meters per second just (usually) means how many meters are traversed by an object each second. Simple.
But I don't really have a mental conception of what it means when units are multiplied, e.g. a kilogram-meter. Can anyone explain in simple physical terms what a kilogram-meter is?
Answer
A kilogram-meter doesn't have an intuitative physical significance. Laar's product examples are meaningful for composite units like force or volts, but when dealing with products of basic units like kg, m, s, moles, amperes, physical meaning seems to only occur when there's a divisor like seconds, per your comments. So for example, kilogram-meter without a second divisor (for momentum) is intuitively meaningless.
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