# Inertial and non-inertial frame of reference

Okay, so I know what inertial and non-inertial frames of reference are:
1. Inertial is when Newton's laws of motion hold.
2. Noninertial is when they do not hold (the object is accelerating without a force).

And I have a few examples as well, such as when you are is in a car and the car is accelerating. Then you move forward. If you are inside the car, you are in an inertial frame of reference, but if someone outside is watching you move forward, it is a non-inertial frame of reference because in their POV, there is no force acting on you.
Or when you are in an airplane and you have a yo-yo in your hand. The yo-yo moves to the side even when you did nothing due to the acceleration of the plane (inertial frame), and if someone sees this from the outside (not possible, but IF that could happen), it is a non-inertial frame of reference.
Or if someone is juggling inside a car. It is just as easy (or just as difficult) to juggle balls in a room which is standing still as it is to juggle in a bus which is traveling smoothly down a straight road at constant speed. (Disregard problems with elbow room on the bus, or imagine one with no seats in it.) In fact, the juggler on the bus could not determine that the bus was moving based on any clues gathered from the motion of the balls. They would move through the air within the moving bus exactly as if they were being tossed about within the still room - as long as the bus traveled smoothly down a straight road at constant speed; that is, as long as the bus moved with a constant velocity.

The point is, I understand what inertial and non-inertial frame of reference is (to a degree), but I need to think of some more examples where inertial and non-inertial frames of reference are present and they're supposed to be "creative", but I cannot think of anything and that's where I need help.

cepheid
Staff Emeritus
Gold Member
Welcome to PF!

1. Inertial is when Newton's laws of motion hold.
2. Noninertial is when they do not hold.

Yes

And I have a few examples as well, such as when you are is in a car and the car is accelerating. Then you move forward. If you are inside the car, you are in an inertial frame of reference, but if someone outside is watching you move forward, it is a non-inertial frame of reference because in their POV, there is no force acting on you.

I'm sorry, but you have this backwards. The accelerating car is the non-inertial frame of reference. The observer on the road is in an inertial frame. Accelerating frames are always non-inertial. Inertial frames move with constant velocity.

Here is the reasoning.

Let's say that in this case, "accelerating" means moving in a straight line with increasing speed.

From the point of view of an observer on the road (i.e. in a frame of reference in which the road is stationary), there is an unbalanced (or net) force* acting on the driver, and the driver is accelerating. Therefore Newton's second law is being obeyed.

*In this case, the force on the driver is the normal force from the contact with the seat back.

However if we consider the frame of reference of the driver, what we're saying is that we're going to consider the driver to be stationary. That's problematic from the driver's point of view, because he "knows" that he is stationary, and that Newton's 2nd law dictates that there should be no net force on him. Yet, he can feel a force from the back of the seat pushing him forwards. So, a force is acting on him and yet he is not accelerating (in this frame). Newton's laws seem to have broken down.

The way to fix things and save Newton's laws is to introduce a "fictitious force" that is slamming the driver back into his seat. If the driver considers that this force is acting, then suddenly things make sense. The force pushing him into the seat is exactly counteracted by the force of the seat pushing back on him, the two forces are balanced, and as a result, he does not accelerate.

This force is "fictitious" in the sense that nothing is physically exerting that force, it is just there seemingly for no reason. It arises solely as a consequence of considering things from a non-inertial (accelerating) reference frame. However, the force is there in the sense that if you've ever been in a car when somebody slammed on the gas pedal, then you've certainly felt it.

Welcome to PF!
Thank you! (:

I'm sorry, but you have this backwards. The accelerating car is the non-inertial frame of reference. The observer on the road is in an inertial frame. Accelerating frames are always non-inertial. Inertial frames move with constant velocity.

That would mean I made a mistake about the airplane as well, right? If the yo-yo moved to the side due the movement of the plane, that would mean the yo-yo is in a non-inertial frame, right? And if someone saw this from outside the plane, they would be in an inertial frame of reference?

Here is the reasoning.

Let's say that in this case, "accelerating" means moving in a straight line with increasing speed.

From the point of view of an observer on the road (i.e. in a frame of reference in which the road is stationary), there is an unbalanced (or net) force* acting on the driver, and the driver is accelerating. Therefore Newton's second law is being obeyed.

*In this case, the force on the driver is the normal force from the contact with the seat back.

I'm confused though. How would the observer know that a force was acting on on the driver?

What if someone was in a bus with roller-skates on. If the bus came to a halt, there would be a force that acted on the person with skates causing them to move forward. In their point of view, they would know that some force acted on them that caused them to move forward, right? But if an observer on the road saw them, it would just seem like they moved by their self, wouldn't it? Who would be in what frame of reference in that case?

cepheid
Staff Emeritus
Gold Member
I'm confused though. How would the observer know that a force was acting on on the driver?

The observer knows that the car is accelerating, and he knows what the cause of that is (the force from the engine). He can see that the driver is inside the car, and is accelerating at the same rate as the car. It stands to reason that a contact force between the car and driver is causing the driver to accelerate along with the car, rather than being "left behind."

What if someone was in a bus with roller-skates on. If the bus came to a halt, there would be a force that acted on the person with skates causing them to move forward.

That depends on which observer you ask, but I should point out that there is NO such force on the roller skater in any inertial frame of reference.

From the point of view an observer in the road frame (which, for our purposes, is an inertial frame), the bus and the roller skater within it were initially moving forwards at a constant velocity. Then the bus driver applied the brakes. The bus began to slow down, but the roller skater didn't. Because of his inertia, he kept on going forwards at the same speed as he was before. This makes sense to the observer on the road. The roller skater appears to be obeying Newton's first law. In the absence of any forces, the skater continues with motion in a straight line at a constant speed. The bus is also obeying Newton's second law. A braking force is being applied, causing acceleration in the direction opposite to the original motion, causing the forward speed to decrease. So, as far as the observer on the road is concerned, everything is moving in accordance with Newton's laws.

Remember I said that inertial frames move relative to each other at a constant velocity? For this reason, the roller skater's frame of reference is also inertial (because he is moving at a constant speed relative to the road frame). So, in the roller skater's frame, obviously the skater is stationary. Initially, the bus is stationary with respect to him, and everything else outside of it is moving backwards past him at a constant speed. But then, suddenly, the bus begins to accelerate in the rearward direction as well, so that it is no longer stationary relative to the skater. So, everything else is still moving past him, and now so is the bus. From his point of view, this makes sense, because he knows that a braking force has been applied to the bus, which is why it started accelerating past him in the rearward direction. As far as the skater is concerned, the bus is obeying Newton's second law by accelerating in the direction of the net force that is being applied to it. Notice that the two inertial observers agree on what is physically going on here.

It's only in the frame of reference of the bus that things appear to be really weird. This is an accelerating (non-inertial) frame of reference. From the point of view of the passengers on the bus, since they think that they are stationary, it is very strange that the roller skater suddenly starts to accelerate forwards (as does everything else in the world). This acceleration has no apparent cause. The motion does not seem to be in accordance with Newton's laws. Only by introducing a force that pushes the skater forward can they reconcile the observed motion with Newton's laws. This is the same force that seems to be trying to push them forwards out of their seats, although in their case it is counteracted by friction/them grabbing on to something.

If all this seems complicated, just remember what I said before:

cepheid said:
Accelerating frames are always non-inertial. Inertial frames move with constant velocity.