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Intuitively (at least to me) it seems that the answer should be "yes", since a fictitious force arises due to being in a non-inertial frame; the frame is accelerating, but the objects within this frame (neglecting any other forces) and so they will remain at rest (or at constant velocity), however, relative to an observer in this non-inertial frame, they will all seem to accelerate in the opposite direction at the same rate.

If the above is correct, then this notion can be shown mathematically as follows (at least, I think). Newton's 2nd law states that the acceleration, $\mathbf{a}$ of a massive object (due to an applied force) is proportional to the force, $\mathbf{F}$ acting on it, such that $\mathbf{F}=m\mathbf{a}$, where the mass $m$ of the object is the constant of proportionality. This does not define the force (by which I mean it doesn't give a mathematical expression describing the force, for example, the Coulomb force is defined by the mathematical expression $\mathbf{F}_{C}=\frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}q_{2}}{r^{2}}\hat{\mathbf{r}}$ which is equal to $m\mathbf{a}$). However, in the case of a fictitious force, $\mathbf{F}_{fic}$, the force is defined by the mathematical expression $\mathbf{F}_{fic}=-m\mathbf{a}_{inert}$, where $\mathbf{a}_{inert}$ is the acceleration of the reference frame. It has this form since it is introduced to account for the acceleration of the reference frame. Then, by Newton's 2nd law, assuming that no other forces are acting, we have that $$-m\mathbf{a}_{inert}=m\mathbf{a}\Rightarrow\mathbf{a}=\mathbf{a}_{inert}$$ i.e. the acceleration of each of the objects due to this fictitious force is independent of its mass.

I'm unsure though whether I've conducted this analysis completely correctly though, so any feedback would be much appreciated.

user35305
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  • It seems like you're really asking whether fictitious forces are proportional to mass in general. Or, equivalently, whether acceleration due to fictitious forces is independent of mass. – Brionius Apr 14 '16 at 23:54
  • @Brionius Yes, that is what I'd like to check my understanding of. Would what I put be correct at all? It seems that by definition the acceleration did to the fictitious force should be independent of mass since it is introduced to account for the fact that the reference frame itself is accelerating, and hence all objects within it are being accelerated at the same rate by virtue of being in this frame. – user35305 Apr 15 '16 at 07:38

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The acceleration of an object by fictitious forces is by the definition of what a fictitious force is due to the acceleration of the non inertial reference frame only and does not depend on its mass.

In order to make Newtonian mechanics work in those non inertial frames these fictitious forces are introduced and defined to be equal to the mass times the acceleration of the non inertial frame.

See for example: How fictitious are fictitious forces?

Community
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Jan Bos
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  • OK, so am I correct at all in what a wrote? Each object within the frame experiences the same acceleration independently of its mass relative to an observer in a given non-inertial reference frame exactly because it is the frame itself that is accelerating and not the objects within it?! – user35305 Apr 15 '16 at 07:44
  • @user35305 actually that depends on situations like if you have centripetal force then all objects about a certain distance from axis would have the same acceleration as you know $a={\omega}^2R$ when you are on a train thats accelerating then all objects feel the same acceleration but at exactly opposite direction. – Nobody recognizeable Mar 06 '19 at 00:38