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We don't help our students very much by our use of language. How often do
our students hear "the acceleration due to gravity" in the context of little
g? We use units of acceleration on it, too, so it MUST be "the"
acceleration! We're our own enemies.
I have taken to telling my students to "watch their language" when they use
such phrases. Little g is more properly called the local gravitational
constant, and it has a value of 9.8 N/kg, not 9.8m/s^2.
And once again I have to ask: Where is the problem? Maybe I'm