Non-inertial Frames of Reference

[Balsam]

Either the teacher is incorrect or you are interpreting that statement incorrectly. Newton's first law always applies if the frame of reference is inertial. The fact that the car is accelerating does not mean that the road no longer defines an inertial frame of reference.

The frame of reference is the car and the sidewalk. So, from the car's frame of reference is non-inertial, while the sidewalk's is not.

 

[jbriggs444]

Could you please tell us what a frame of reference is?

 

[Balsam]

Could you please tell us what a frame of reference is?

The coordinate plane from which motion is observed.

 

[jbriggs444]

You spoke as if the car and the sidewalk together define a single frame of reference. Was that your intent?

 

[Balsam]

You spoke as if the car and the sidewalk together define a single frame of reference. Was that your intent?

No, I meant to say they are two different frames of reference

 

[jbriggs444]

No, I meant to say they are two different frames of reference

They define two different frames of referernce, yes. Good.

Now you also wrote:

So, from the car's frame of reference is non-inertial, while the sidewalk's is not.

This is a bit garbled, but it seems that you agree that the sidewalk defines an inertial frame of reference.

So does Newton's first law apply in the sidewalk frame?

 

[Balsam]

They define two different frames of referernce, yes. Good.

Now you also wrote:

This is a bit garbled, but it seems that you agree that the sidewalk defines an inertial frame of reference.

So does Newton's first law apply in the sidewalk frame?

Actually, I'm not sure. This whole problem is confusing me because I don't fully understand the lesson and I still don't know how to solve the problem.

 

[jbriggs444]

Actually, I'm not sure. This whole problem is confusing me because I don't fully understand the lesson and I still don't know how to solve the problem.

That's OK. We will get there. The task at hand is to be sure that you have a good enough understanding of reference frames to tackle the problem.

You said that a "frame of reference" is a coordinate plane from which motion is observed. That reasonably accurate. I might have said "coordinate grid" instead. The grid lines define a standard of what is stationary and what is moving. If the ball always stays at the same grid line, it is at rest in the reference frame. If the ball moves from one grid line to another and does so faster and faster over time then the ball is not at rest in the reference frame. We say that it is moving and accelerating in that reference frame.

At the same time we are measuring the ball against a coordinate grid that is tied rigidly to the car, we could also measure the ball against a coordinate grid that is tied rigidly to the sidewalk. Can you see that the ball might be "accelerating" when measured against the car grid and might be "at rest" when measured against the sidewalk grid?

 

[Balsam]

That's OK. We will get there. The task at hand is to be sure that you have a good enough understanding of reference frames to tackle the problem.

You said that a "frame of reference" is a coordinate plane from which motion is observed. That reasonably accurate. I might have said "coordinate grid" instead. The grid lines define a standard of what is stationary and what is moving. If the ball always stays at the same grid line, it is at rest in the reference frame. If the ball moves from one grid line to another and does so faster and faster over time then the ball is not at rest in the reference frame. We say that it is moving and accelerating in that reference frame.

At the same time we are measuring the ball against a coordinate grid that is tied rigidly to the car, we could also measure the ball against a coordinate grid that is tied rigidly to the sidewalk. Can you see that the ball might be "accelerating" when measured against the car grid and might be "at rest" when measured against the sidewalk grid?

Why would it be at rest measured against the sidewalk grid? Is it because the ball accelerating backwards keeps it on the sidewalk grid?

 

[jbriggs444]

Why would it be at rest measured against the sidewalk grid? Is it because the ball accelerating backwards keeps it on the sidewalk grid?

It is not "on" any grid at all. The grids are entirely imaginary. They need have no physical existence.
Imagine a pane of glass strapped to the side of the car where the door would be. On this pane of glass we draw some evenly spaced vertical lines. From the car or from the sidewalk (it does not matter which), we can watch the ball and see that when the car moves, the ball does not stay lined up with any single vertical line on the moving glass.

Imagine on the other side of the car we remove the door. We erect a pane of glass with evenly spaced vertical lines.This pane of glass is attached to the sidewalk. When the car starts moving we look to see whether the ball stays lined up with one of these lines. We can look from the car or from the sidewalk. It does not matter which.

Is it possible for a ball to be stationary compared to one of the lines on the sidewalk glass while appearing to move backwards compared to the lines on the car glass?

 

[Balsam]

It is not "on" any grid at all. The grids are entirely imaginary. They need have no physical existence.
Imagine a pane of glass strapped to the side of the car where the door would be. On this pane of glass we draw some evenly spaced vertical lines. From the car or from the sidewalk (it does not matter which), we can watch the ball and see that when the car moves, the ball does not stay lined up with any single vertical line on the moving glass.

Imagine on the other side of the car we remove the door. We erect a pane of glass with evenly spaced vertical lines.This pane of glass is attached to the sidewalk. When the car starts moving we look to see whether the ball stays lined up with one of these lines. We can look from the car or from the sidewalk. It does not matter which.

Is it possible for a ball to be stationary compared to one of the lines on the sidewalk glass while appearing to move backwards compared to the lines on the car glass?

I think it is possible for it to be stationary because the distance it accelerates backwards would make up for the distance that the car is accelerating forward. Thus, it will stay in the same position on the sidewalk glass

 

[jbriggs444]

I think it is possible for it to be stationary because the distance it accelerates backwards would make up for the distance that the car is accelerating forward. Thus, it will stay in the same position on the sidewalk glass

Yes.

If we describe the situation from the car's point of view, the ball, the sidewalk and the sidewalk's glass grid are all are accelerating rearward at the same rate. If we describe the situation from the sidewalk point of view, the ball is stationary and both the car and its glass grid are accelerating forward.

Now, if the ball is stationary relative to the sidewalk and if is subject to no net force, might it be reasonable to guess that the sidewalk (and its glass grid) define an inertial frame?

 

[Balsam]

Yes.

If we describe the situation from the car's point of view, the ball, the sidewalk and the sidewalk's glass grid are all are accelerating rearward at the same rate. If we describe the situation from the sidewalk point of view, the ball is stationary and both the car and its glass grid are accelerating forward.

Now, if the ball is stationary relative to the sidewalk and if is subject to no net force, might it be reasonable to guess that the sidewalk (and its glass grid) define an inertial frame?

Yes, it would be an inertial frame. But, what about the ball's motion relative to the car? It's a non-inertial frame, so there must be a fictitious force acting on the ball. Do you have to draw the fictitious force in the FBD?

 

[jbriggs444]

I would say yes, draw the fictitious force.

 

[Balsam]

I would say yes, draw the fictitious force.

Thank you.