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Re-post the question by complementing the inaccurate information.

First, I'm just an ordinary person who's interested in physical phenomena and physics. I apologize for not expressing it through accurate formulas or symbols.

Let's consider the situation where the bus is moving at constant speed and then suddenly accelerating at acceleration 'a'.

The bus handle is attached to the ceiling of the bus through a string or thread as shown in the picture. I'll attach the ugly drawing

enter image description here

If the mass of the handle is 'm', the net force of the handle is the same as 'ma' when observed from inertial system(outside of the bus). Let's say the center of mass of the handle is 'Cm' and let's say one point of the bus is A. If the acceleration acting on the bus and the handle is all the same from the start of the acceleration, shouldn't the relative positions of Cm and A not change? However, as a result, the center of mass of the handle is further behind.

Which means that the net force acting on the center of mass of the handle is not 'ma' while the handle is tilted from the start of acceleration and become equilibrium ? TWo objects have the same initial speed, the same initial position, the same acceleration.. do not seem to have a relative change in position between the center of mass of the handle and the point fixed to the bus.

I don't think the net force acting on the handle will be 'ma' until it reaches equilibrium as it slips back. How can I calculate it?

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    $\begingroup$ The system is not clear to me. What is "the handle", how is it attached to the bus and the rope, etc.? A diagram would help $\endgroup$ Jan 13, 2023 at 16:49
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    $\begingroup$ Sorry for the lack of explanation. The handle is suspended by a string. Tension works. $\endgroup$
    – NOH WHIREA
    Jan 13, 2023 at 17:55
  • $\begingroup$ Can you clarify what your question is about the above? $\endgroup$
    – BowlOfRed
    Jan 13, 2023 at 18:23
  • $\begingroup$ See if the answers to physics.stackexchange.com/q/616541 $\endgroup$
    – John Darby
    Jan 13, 2023 at 19:10
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    $\begingroup$ The bus handle is attached to the ceiling of the bus through a string or thread as shown in the picture. I'll attach the picture. I'm sorry. $\endgroup$
    – NOH WHIREA
    Jan 14, 2023 at 2:48

2 Answers 2

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The door of the bus applies the net force necessary to accelerate the handle.
It does this by the handle moving relative to the door which compresses the door on one side of the handle and stretches the door on the other side.
The door is elastic and you can think of there being “molecular springs” on either side of the handle being compressed on one side and stretched on the other.

So the door has to deform to apply a force on the handle to accelerate it, ie the centre of mass of the handle moves relative to centre of mass of the door.

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While the bus is accelerating forwards the handle is displaced backwards. The force exerted on the handle by the string therefore has a forwards component, as a diagram will show. It is this forward force component that gives the handle its forward acceleration!

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