I asked on twitter what people might name inverse mass. Here’s what I got so far
Alacrity (@bvancil):
Mechanical Conductivity (@kellyoshea):
Capriciousness (@almeidaphysics):
Ertia (@fnoschese):
Mobility (@chrisgoedde):
Breeze (@chrisgoedde):
Wisp (@chrisgoedde):
Dispatch (@chrisgoedde):
Coefficient of Acceleration (@calcdave)
Force Responsitivity (@brianwfrank)
What do you like? What you would add?
Added from the comments
Acceleration propensity (LJ Atkins)
Acceleration susceptibility (LJ Atkins)
Influentia (LJ Atkins)
Accelerability (Dan Goldner)
Teach. Brian. Teach. 
Ertia!
Acceleration propensity. Or Acceleration susceptibility? or influentia? (The metaphor that first jumped to mind when considering 1/m was a teenage girl who is all too easily influenced – hence “influentia.”)
I actually really like force responsivity, too. But for some reason, I feel like the name should have to do with acceleration and not force.
And I really like this game.
Accelerability? (though I like Alacrity better…)
I like this whole idea. What if we asked students to name the constant of proportionality in every relationship we find? I always found my students had some difficulty with the notion of spring constant when we first found the relationship between force and stretch, but I think this might have been eased a bit if I gave them some time to devise a name for this quantity on their own before telling them them canonical name.
Don’t forget to invent a unit! We do have Hz=s⁻¹, after all. My vote is for units of alacrity [m⁻¹]=kg⁻¹=celer. Then 1 m/s/s per 1/kg is “1 unit of acceleration for each 1 celer “.
“cel” might work too. Celer is Latin for swift, just like gram is latin for small weight (from http://latindictionary.wikidot.com/adjective:celer )
I’d also like to propose “motility” as a variation of @chrisgoedde’s suggestion. Or, to shorten your suggestion, “forceability”, a responsiveness to force.
To collect my thoughts on John Burk’s thoughts, with which I agree but have a hard time coming up with something general but more descriptive than:
(Y) = (Y-per-X constant) (X)
(force of gravity) = (gravitational strength constant, i.e. gravitational fieldstrength) (gravitational charge, i.e. mass)
(electric force) = (electric charge) (electric fieldstrength)
(spring force) = (spring response constant) (spring displacement)
(acceleration) = (alacrity constant) (force)
(force) = (inertial constant) (acceleration)
(circumference of circle) = (circumference growth constant) (radius of circle)
My terms could definitely use some cleaning up!
Chris actually suggested motility. I didn’t include it because it already has a technical definition in biology.
I agree with you that we need a unit as well.
celerity is bad name for 1/kg, becasue in it is already used in oceanography for
the speed of individual waves (as opposed to the speed of groups of waves). See e.g. http://en.wiktionary.org/wiki/celerity
Further considerations may be..
inverse of mass is a “metric” for kinetic energy for momentum
T=p^2/(2*m)
like mass itself is a “metric” for kinetic energy for velocity
T=m*v^2/2
A similiar couple is in mechanic stiffness-compliance. Compliance in mechanical science is the inverse of stiffness. The stretch energy is than
U = k u^2/2 = F^2/(2*k)
P.S. I liked the subject. I am thinking for a proper name in Russian.
P.P.S. alacricy – celer so far to my test the best pair name/unit
Another problem is that arithmetic operation are clearly defined for mass. Working with inverses is a mess. Adding 2 equal masses result in double mass whereas inverse is halved.
Inverse of a mass matrix is often used in structural mechanics, but it does not have special name.
I’ve never encountered such concept either in English or Russian literature. I think in English “agility” fits well. In Rissian I can’t make up anything better than “подвижность” or “респонсивность”. “Подвижность” implies a wrong idea that it is velocity who is proportional to it, not acceleration. “Респонсивность” doesn’t have this flaw, but it is used so rarely, that one can say this is not a proper Russian word, but just a mistranslation from English.
Thanks!
I like the idea of “agility” because this is the word that occurred first to me for this issue. For a given applied force, the object accelerate better for a larger “agility,” that is, when the inverse mass is larger.
Finally, I found the name in literature the name “mobility matrix” for inverse of mass matrix.
Advanced structural dynamics, Donea, 1980
http://books.google.de/books?hl=ru&id=jtdRAAAAMAAJ&q=%22mobility+matrix%22#search_anchor
That’s cool. And totally makes sense.
I call inverse mass “vass”, as in (in)v(erse)+(m)ass. Vass is also similar to “vast” because a larger value is like a mass spread out.