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If a bus stops moving suddenly, we tend to fall forwards due to the inertia of motion of our upper body. But can we explain the sudden jerk in the forward direction due to some pseudo force? (Because I think according to an observer on the ground [inertial frame], the bus is a non-inertial frame {it is accelerating} - therefore pseudo force can be applied).

But can we show this sudden jerk in the forward direction due to pseudo force?

Inertia of Motion of person in train

Like this image showing this phenomenon in the train? [How can pseudo force be applied here instead of the inertia of motion].

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    $\begingroup$ From the perspective of an observer in the bus, the pseudo force is zero while the bus is moving at constant velocity, then, as it starts breaking, the pseudo force appears out of nowhere (has no obvious source), and grows quickly to some value, lasts a short while, then drops back to zero when the bus stops. The forward acceleration of any object is then attributed to this pseudo force. $\endgroup$
    – Filip Milovanović
    Commented Jul 5, 2022 at 16:24
  • $\begingroup$ Can you write as an equation using the mass and acceleration? $\endgroup$
    – Tom Henderson
    Commented Jul 5, 2022 at 16:35
  • $\begingroup$ In a non-inertial reference frame, the apparent force is the sum of all the forces, including the pseudo force $F_p$. So, in this case, the pseudo force, the force of gravity, the normal force and the tension from the bus-straps: $F = F_p + F_g + N + T = ma$ (assuming the person is a rigid body). If this was a person floating in an accelerating spaceship, the pseudo force would just be $ma$, for the person's acceleration measured from the POV of the spaceship itself. In a bus, it gets more complicated because $F_p + F_g$ combine to pull you at an angle, and $T$ varies with time. $\endgroup$
    – Filip Milovanović
    Commented Jul 5, 2022 at 17:38

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If a bus stops moving suddenly, we tend to fall forwards due to the inertia of motion of our upper body. But can we explain the sudden jerk in the forward direction due to some pseudo force?

Our inertia is the pseudo force. It's called an inertial force. It is pseudo (fictitious) because there is nothing making contact with us pushing us forward. Our bodies move forward during braking because our inertia wants to keep us moving forward, instead of stopping.

Hope this helps.

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    $\begingroup$ "because there is nothing making contact with us pushing us forward" - but that would disqualify all the fundamental forces of nature (as they are contactless - act at a distance). It's that there's no physical origin of the force, and the fact that it vanishes in an inertial frame, that makes it fictitious. $\endgroup$
    – Filip Milovanović
    Commented Jul 5, 2022 at 17:45
  • $\begingroup$ @FilipMilovanović The “inertial force” is not a fundamental force and clearly no non contact fundamental forces (gravitational, electromagnetic etc,) forces are involved here. $\endgroup$
    – Bob D
    Commented Jul 5, 2022 at 18:24
  • $\begingroup$ Clearly, at least gravity is involved in this situation. But that's not the point, you offered a method to identify inertial forces without qualifying it in any way - or, at least, the OP could see it that way. Don't you think that could confuse the OP, or even worse, potentially become a seed for a misunderstanding that will hinder them in their studies? It's good when you can make things simple, but there's a danger in being too handwavy. $\endgroup$
    – Filip Milovanović
    Commented Jul 5, 2022 at 18:43
  • $\begingroup$ @FilipMilovanović gravity is not involved with jerking forward which is what the OP is asking. The inertial force is only needed in the non inertial frame of the bus. In the inertial frame of the ground there is no need to use a pseudo force to explain the person moving forward. That’s what they’re doing. Why don’t you post an answer of your own. In the meantime let the OP be the judge if I’m “confusing” him $\endgroup$
    – Bob D
    Commented Jul 5, 2022 at 19:01
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    $\begingroup$ I see - it's a case of miscommunication then. I didn't mean to imply such an intent on your part (on the contrary, it was an appeal to your good intentions). I used "handwavy", which doesn't have the connotation you quoted (and is in fairly common use in education and academia, so I didn't think anything of it); it just means stating something without discussing subtleties or going into detail. "Handwavy [demonstration/proof/explanation] - one omitting important details or logical steps, perhaps instead appealing to laymen, common sense, tradition, intuition, or examples". $\endgroup$
    – Filip Milovanović
    Commented Jul 6, 2022 at 0:20

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