# The relation between acceleration and inertial force

Acceleration causes inertial force, and it is not relative, but why?
What is the reason for feeling inertial force by acceleration?

Inertial forces, also known as pseudo-forces or fictitious forces, appear in accelerating reference frames; the inertial obsever sees their action - centrifugal forces, Coriolis forces, Euler forces, as well as responses to simple acceleration.

The pseudo-force laws all appear in the form of Newton's Second Law of Motion, F=ma.

The occupant of the spinning teacup feels the centrifugal force! It is prportional to their mass. They also respond to the sudden stopping of a car, hence the utility of air bags.

D'Alembert was the first to devote extended effort to analyze inertial forces. His results paved the way for analytical mechanics.

Einstein, while working on the puzzle of how to fit gravitation into the framework of Special Relativity, noted that Newton's Universal Law of Gravitation was of the same D'Alembertian form, decided that gravitation must also be a pseudo-force, starting him on the long path to General Relativity.

So, in conclusion, pseudo-forces always appear linear in the mass and the acceleration. As Isaac Newton noted in his famous whirling bucket experiment, acceleration is always absolute with respect to every inertial reference frame.

• Ok I make the question more clear: – Reza Feb 23 '16 at 6:57
• Is there still a question? I've explained how it works. The why is that it is consistent with the laws of motion. – Peter Diehr Feb 23 '16 at 11:33

You don't feel "inertial force". What you feel is the friction of the floor on your shoes, or the side of your car pressing against your body. These are perfectly real forces caused by the non-uniform motion of something in your environment interacting with you as your inertia tries to keep you in uniform motion.

• Is there a physical reason for the inertial force ? – Wang Yun Feb 21 '16 at 4:18
• Hello. A question if I might: When we accelerate, don' t we feel a force opposite to the direction of acceleration, in our reference frame? Thank you. – Constantine Black Feb 21 '16 at 10:21
• @ConstantineBlack Yes. Note that I'm focusing on the word feel that the OP used, making a distinction from the word observe. What is the agent of the force that you feel? In an accelerating elevator, it is the floor producing a greater normal force on your feet. In a cornering car it's friction between the seat of the car and your back and bottom. If you were floating in a spaceship which begins to accelerate, you would observe that your path is non-uniform in the frame of the spaceship, but you would feel no force at all. – garyp Feb 21 '16 at 12:32
• OK I make the question more clear: point X and Y in space are getting far from each other with acceleration (a). If they move by a constant velocity there is no difference between X and Y but when they get apart by acceleration only on the real moving mass we will observe or feel inertial force. The question is "why" not "how" – Reza Feb 23 '16 at 7:13
• @Reza What do you mean by "real moving mass"? I'm afraid I still don't understand the question. Perhaps someone else does? I recommend editing your original post. It will then get more views. – garyp Feb 23 '16 at 11:48