How fictitious are fictitious forces?

Question

How fictitious are fictitious forces?

More specifically, in a rotating reference frame i.e. on the surface of the earth does an object that is 'stationary' and in contract with the ground feel centrifugal and Coriolis forces? Or are these forces purely fictional and used to account for differences in observed behaviour relative to an inertial frame?

To give a practical example a turreted armoured vehicle is sitting stationary and horizontally somewhere in the UK. The turret is continually rotating in an anti-clockwise direction. Do the motors that drive the turret's rotation require more power as the turret rotates from east to west and less power as the turret rotates from west to east? i.e. are the turret motors cyclically assisted and hindered by the earths rotation?

Answer 1

No, they are not real forces.

Quoting from my answer here

Whenever we view a system from an accelerated frame, there is a "psuedoforce" or "false force" which appears to act on the bodies. Note that this force is not actually a force, more of something which appears to be acting. A mathematical trick, if you will.

Let's take a simple case. You are accelerating with $\vec{a}$ in space, and you see a little ball floating around. This is in a perfect vacuum, with no electric/magnetic/gravitational/etc fields. So, the ball does not accelerate.

But, from your point of view, the ball accelerates with an acceleration $-\vec{a}$, backwards relative to you. Now you know that the space is free of any fields, yet you see the particle accelerating. You can either deduce from this that you are accelerating, or you can decide that there is some unknown force, $-m\vec{a}$, acting on the ball. This force is the psuedoforce. It mathematically enables us to look at the world from the point of view of an accelerated frame, and derive equations of motion with all values relative to that frame. Many times, solving things from the ground frame get icky, so we use this. But let me stress once again, it is not a real force.

And here:

The centrifugal force is basically the psuedoforce acting in a rotating frame. Basically, a frame undergoing UCM has an acceleration $\frac{mv^2}{r}$ towards the center. Thus, an observer in that rotating frame will feel a psuedoforce $\frac{mv^2}{r}$ outwards. This psuedoforce is known as the centrifugal force.

Unlike the centripetal force, the centrifugal force is not real. Imagine a ball being whirled around. It has a CPF $=\frac{mv^2}{r}$, and this force is the tension in the string. But, if you shift to the balls frame (become tiny and stand on it), it will appear to you that the ball is stationary (as you are standing on it. The rest of the world will appear to rotate). But, you will notice something a bit off: The ball still has a tension force acting on it, so how is is steady? This balancing of forces you attribute to a mysterious "centrifugal force". If you have mass, you feel the CFF, too (from the ground, it is obvious that what you feel as the CFF is due to your inertia)

What really happens when you "feel" psuedoforces is the following. I'll take the example of spinning on a playground wheel.

From the ground frame, your body has inertia and would not like to accelerate(circular motion is acceleration as the direction of velocity changes).

But, you are holding on to the spinning thingy so you're forced to accelerate. Thus, there is a net inward force--centripetal force--a true force since it's from "holding on". In that frame, though, you don't move forward. So your body feels as if there is a balancing backwards force. And you feel that force acting upon you. It really is your body's "inertia" that's acting.

Yes, the turret's wheels are affected. Again, this is due to inertia from the correct perspective, psuedofoces are just a way to easily explain inertia.

Remember, Newton's definition of a force is only valid in an inertial frame in the first place. Psuedoforces make Newton's laws valid in non inertial frames.

Answer 2

Centrifugal and Coriolis forces are indeed so called pseudo forces that account for differences in observed behaviour relative to an inertial frame.

So if you see an object standing on the surface of the Earth, you can be sure that static friction is holding it at rest relative to Earth's surface.

Great example of the effect of pseudo forces is so called Foucalt's pendulum. Since there is no static friction for pendulum, pendulum's plane of oscillation rotates. Foucalt's pendulum is also a proof that Earth is not an inertial frame of reference.

The problem of observing pseudo forces is in the fact they are very small compared to gravity. Centripetal acceleration due to rotation of the Earth around its axis is of the order $10^{-2}$ m/s$^2$ (depending on the position), while centripetal acceleration due to rotation of the Earth around Sun is $6 \times 10^{-3}$ m/s$^2$. So you have an effect when rotating a turret, but I doubt you would be able to measure it.

So what makes forces pseudo? Well, you might have heard that Newton's laws are valid only in inertial frame of reference. If you watch the movement of the turret from outside the Earth (inertial frame of reference), you can observe that turret is making complex movements and constantly accelerating. Gravitational and frictional forces acting on turret are responsible for these movements.

However if you are standing on the Earth it seems to you that turret is at rest. But gravitational and frictional forces are still acting on it, so this does not add up. The sum of forces different than zero, and turret at rest, breaks 2nd Newton's law! 2nd Newton's law is no longer valid because you are no longer in inertial frame of reference.

In order to "patch" 2nd Newton law in non-inertial frames of references, you introduce pseudo forces. After introduction of pseudo forces, 2nd Newton law is valid even if you are no longer in inertial frame of reference. You can feel those forces only because your intuition requires additional forces in order to explain your observations.

Answer 3

In classical mechanics it makes sense to distinguish between fictitious forces caused by accelerating coordinate systems and "real" forces in inertial frames, but this is no longer the case in general relativity.

In general relativity except in simple cases there are generally no preferred global reference frames, and gravity in some sense becomes indistinguishable from the Newtonian concept of a pseudoforce.

You can take your pick as to whether this means that gravity is less real or pseudoforces are more real, but it's not a physics question to worry about the answer.

Answer 4

Place a stationary object on a piece of graph paper and accelerate the graph paper anyway you want over time, while recording the position of the object on the graph paper and keeping the object stationary relative to you:

Q: Did you see the object accelerate while you were moving the graph paper?

A: Nope, so there isn't a physical force on it.

Q: What is the trajectory of the object on the graph paper and your conclusion?

A: The trajectory is a curve and so it was accelerating in the coordinate system of the graph paper. We can model this as an unphysical force acting upon the object in this coordinate system. This fictitious force will depend upon how this coordinate system is accelerating wrt one moving at a constant velocity.