# I Principle of Equivalence

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1. Oct 12, 2015

### Emilie.Jung

Equivalence principle says that gravitational forces are equivalent physically to inertial forces. Can someone explain what is meant by that and how was it concluded?

2. Oct 12, 2015

### atyy

As an elevator accelerates up, you will feel yourself being pulled down. In this way, one can think of the upward acceleration of the elevator as creating a gravity that pulls you down. Similarly, when the car rounds a corner, you will feel yourself being pushed outward by a force that is like a gravitational force. These forces due to the acceleration of the elevator or car are "gravitational" in the sense that they act on everything in the elevator or the car in the "same" way.

3. Oct 12, 2015

### Emilie.Jung

I was asking about gravitational and inertial forces. You didn't mention anything concerning inertial forces? I also asked about their equivalency. I would appreciate if you would explain that. @atyy

Last edited: Oct 12, 2015
4. Oct 12, 2015

### atyy

An inertial force is a force that is due to being in an accelerated frame, eg. the elevator accelerating upwards or the car rounding a corner.

5. Oct 12, 2015

### Staff: Mentor

Both are proportional to mass and neither can be detected using an accelerometer.

6. Oct 12, 2015

### Emilie.Jung

7. Oct 12, 2015

### Staff: Mentor

Sure, what more would you like to know?

8. Oct 13, 2015

### Emilie.Jung

What do you mean by neither can be detected using an accelerometer? And yes, what if they are both proportional to mass? How do those relate to my question? Thank you.

9. Oct 13, 2015

### Staff: Mentor

Consider an accelerometer at rest on the ground. There is an upwards contact force and a downwards gravitational force. These two forces cancel each other, but the accelerometer reading is non zero. It detects only the upwards contact force.

Similarly, consider an accelerometer at rest in the rotating reference frame of a centrifuge. There is an inwards contact force and an outwards inertial force. These two forces cancel each other, but the accelerometer reading is non zero. It detects only the inwards contact force.

10. Oct 17, 2015

### loislane

Inertial acceleration can't be detected using an accelerometer? How else can an observer with no other external inputs know that its frame is non-inertial?

11. Oct 17, 2015

### Staff: Mentor

By the fact that he observes motion that can only be explained by forces that are not detected by the accelerometer.

12. Oct 17, 2015

### loislane

Huh? But if its accelerometers marks zero acceleration then it is in an inertial frame by definition, why should it feel inertial forces?

13. Oct 17, 2015

### Staff: Mentor

Suppose you are in a non inertial lab which is accelerating uniformly in a direction that we will call "up".

Inside the lab you can throw an accelerometer and see that it travels on a parabolic path. Because of the motion you know it is acted on by a downwards pointing force. However, that force is not detected by the accelerometer as it reads 0 during the motion.

Because of the existence of this force which is detectable by the motion, but not measured by the accelerometer, you know that the lab's frame is non inertial.

Last edited: Oct 17, 2015
14. Oct 17, 2015

### loislane

So you are saying that an accelerometer attached to a noninertial lab that is uniformly accelerating doesn't detect the inertial force felt by a person on that lab? This is what we are discussing here.

15. Oct 17, 2015

### Staff: Mentor

I am saying that an accelerometer does not detect inertial forces.

The circumstances don't matter. It doesn't matter if the accelerometer is at rest or moving in the non inertial frame. It doesn't matter if the frame is uniformly accelerating or undergoing some more complicated motion.

The same is true of gravity. An accelerometer does not detect gravity either. That is one of the reasons that they are considered equivalent.

16. Oct 17, 2015

### A.T.

You cannot "feel" inertial forces, for the same reason accelerometers cannot detect them.

17. Oct 17, 2015

### loislane

I guess we must be understanding different things by inertial force.
When riding in a bus at constant rectilinear speed I consider myself not feeling any inertial forces. When the bus becomes a noninertial frame by accelerating or taking a turn I consider the forces I feel(like being pulled back or sideways respectively ) as inertial forces,hace you never felt those?

18. Oct 17, 2015

### Staff: Mentor

What you feel is the perfectly normal contact force of the bus pushing back on you, not any "inertial force" causing you to move relative to the bus.

The bus isn't really a good example because it isn't a true inertial frame; you always have the force of the floor of the bus pushing up on you. That makes it difficult to distinguish when the push changes because of the bus turning or accelerating. For a better experiment, imagine yourself floating in a spaceship in low Earth orbit, when the engines suddenly fire for an orbit change. You won't feel any force (and an accelerometer, strapped to you, won't register any reading) at the instant the engine fires, even though, at that instant, the ship becomes a non-inertial frame and you start moving relative to it due to "inertial forces". You will only feel a force when some part of the spaceship pushes on you.

19. Oct 18, 2015

### A.T.

As Peter said, the forces that you actually feel, are frame independent real contact forces and stresses in your body. That you feel them is a frame independent physical fact, so it cannot be related to frame dependent inertial forces. When you analyse the bus from an inertial frame, then there are no inertial forces anymore, but the people in the bus are still squeezed.

What you can attribute to inertial forces is the visually observed coordinate acceleration of people relative to the bus, but not the felt proper acceleration.

20. Oct 18, 2015

### stevendaryl

Staff Emeritus
Peter and A.T. have already addressed this, but I would like to expand on it. Suppose you are in a very large spaceship floating in deep space. You are floating above the floor of the spaceship (there's no gravity). Now, suddenly the spaceship's rockets fire, and it starts accelerating. What do you feel? You feel nothing at all. You just start moving toward the rear of the spaceship. You don't feel any forces until you hit the floor of the spaceship. At the point, what you feel is the force of the floor slamming into you---in other words, you feel contact forces between you and the floor. There is never a time when you feel any inertial forces.