I frequently hear people say something scales with the mass m, or the length l, etc.

What does that mean?

Let's take a concrete example, the force equation F = ma.

Does this mean that F scales with m?

Or, if we have something like moment of inertia = $I = l^2$ * ...

where l denotes the length of a solid, then do we say that " the moment of inertia scales with $l^2$"?

  • 4
    $\begingroup$ A number of comments that weren't going anywhere useful deleted. The best response to a comment you don't care for on a personal level is to either flag it or not but then move on. No one is going to win the internet in the comments. $\endgroup$ – dmckee --- ex-moderator kitten Sep 3 '17 at 23:51

Unmodified the phrase probably means "is proportional to", but it can be modified to mean other functional relationships. For instance "scales quadratically with" or "scales as the square of" indicate a relationship like $$ x \propto y^2\;.$$

In sloppy usage it might mean "depends on" with the functional dependence left unstated (but presumably known to the listener).

Other adjectives that appear with non-trivial frequency include "inversely" "exponentially", "by the inverse square", and "logarithmically". Cubic, quartic, hyperbolic, and other relationships are less common.

| cite | improve this answer | |

In the sense of the Original Post's question, $F=ma$ means (in case you're trying the figure the net force magnitude from the the particle movement) that $F$ scales linearly with both the mass and the acceleration. And the meaning of that statement is that, if the mass were twice larger, than the $F$ should also be (to cause the same acceleration $a$), and if $a$ is ten times larger, than so should $F$.

Similarly, the area of a circle scales with its radius $r^2$, so for a radius 3 times as large, the corresponding area will be $3^2=9$ times larger.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.