# Why Pseudo/Fictious Forces act at centre of mass [duplicate]

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I was reading about torque and pseudo forces and my book says that the torque about centre of mass for a Pseudo/Fictious force is zero.

I cant really get that as it is non-intuitive for me .

Can someone explain it in a simple manner.

Any help is appreciated

## marked as duplicate by AccidentalFourierTransform, ZeroTheHero, Jon Custer, ja72, peterhApr 27 '17 at 2:48

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• Possible duplicate of Why does gravity act at the center of mass? – AccidentalFourierTransform Apr 26 '17 at 16:33
• This is definitely not true for the Coriolis or centrifugal force; they can exert torques about the CM. If you're only considering fictitious forces due to uniform linear motion, then check out the question linked by AccidentalFourierTransform above, especially this answer; the logic is the same as it is for a uniform gravitational field. – Michael Seifert Apr 26 '17 at 16:48

## 1 Answer

While we sometimes think of things as pseudo-forces, they're really better thought of as accelerations (note: I don't have to call them pseudo-accelerations). The pseudo-forces are all results of using non-inertial frames*, which means they have an acceleration term which accounts for the non-inertial effects. For example, the "centrifugal force" in a rotating frame is more accurately a "centrifugal acceleration of $\frac{v^2}{r}$. This term can be derived directly from the change of frame from inertial to rotating, using calculus.

Sometimes it is convenient to choose to think of this effect as a force rather than thinking of it as an acceleration. If we multiply that acceleration by the mass of the object and treat it as a force, we get the exact same equations (it's simple algebra to convert one to the other). This is how we get a pseudoforce.

Now, to answer your question, this effect was best thought of as an acceleration the entire time. This acceleration does not cause the object to rotate about its center of mass. This is why the pseudoforces must always act on the center of mass. If the pseudoforce were to act on any other point, then the pseudoforce would cause a torque. If it caused a torque, it would no longer be a drop-in replacement for the acceleration term.

So in a sense, it's sort of backwards logic. Pseudoforces act on the center of mass because they are a mathematical construct designed to replace another more fundamental effect, and acting on the center of mass is the only way to have a force accomplish this goal.

* All things that I have heard called "pseudoforces" fit this description. If you come across one that does not, we can address it separately.