Introduction to frames of reference

I'd like to do in this video is talk about the notion of a frame of reference, and this is an introductory video. In future videos, we'll go into a lot more depth.

But a frame of reference is really the idea; it's a point of view from which you are measuring things. As we'll see, many of the quantities that we might measure in physics, like velocity or displacement, could be different depending on our point of view, depending on which frame of reference we are measuring from. To get this intuitive grasp of it, I'm going to draw the exact same scenario from three different frames of reference.

That's the first one. This is the second one, and this is the third one. So in this first frame of reference, this first scenario, we're going to talk about the frame of reference of the ground. If you are a stationary observer on the ground, you could imagine this is you here, and you are the person doing the measuring of, let's say, we want to measure velocities.

So from your point of view, since you're stationary relative to the ground, what does the ground's velocity look like? Well, you and the ground appear to be stationary; you appear to not be moving. Now, what if you take out your instruments for measuring velocity, or you see a change in, you see what the displacement is over a certain time for the plane and the car? You're able to see, "Okay, look, this plane has a velocity to the right of 250 m/s."

250 m/s. And let's say this car, that is moving quite fast by car standards, is moving to the left at 50 m per second. So this should be 1/5 of that length. So let me draw it a little bit. So let's say this is moving to the left at 50 m/s. Well, none of this seems crazy. You might be able to go outside next to the highway and see, well, 50 m/s would be quite fast. But anyway, you could observe this type of thing happening; it seems completely reasonable.

But what if we were to change our frame of reference, change the point of view from which we are measuring things? So let's take the frame of reference of the car. Well, in this frame of reference, let's say you're sitting in this car, and I don't recommend you do this while driving. Let's say someone else is driving, or it's an autonomous vehicle of some kind, and you take out your physic instruments with the stopwatch, and you see what the displacement is of the ground and the plane over, say, a second.

You are able to first say from your point of view, you're like, "Well, the car is stationary. The car has a velocity of zero. The car is stationary." From your point of view, you would actually measure the ground to be moving; you would see the trees move past you to the right or behind you if you're moving to the left. So from your point of view, the ground would actually look like it's moving in this direction, in that direction, at 50 m/s.

It would look like it's moving behind you, or in this case, the way we're looking at it, to the right at 50 m/s. Now, what would the plane look like? Well, the plane not only would it look like it's moving to the right at 250 m/s; not only would it be just that 250 m/s, but relative to you, it looks like it's going even faster 'cause you're moving past it. You're going to the left from the stationary, from the ground's point of view, at 50 m/second.

So the plane to you is going to look like it's going 250 plus 50 m/s. So the vector would look like this, and so it would look like it's going to the right at 300. Let me write that in that orange color: at 300 m per second. Now, what about from the point of view of the plane? What if we're talking about the plane's frame of reference? Why don't you pause this video and think about what the velocities would be of the plane, the car, and the ground from the plane's point of view?

All right, now let's work through this together. So now we're sitting in the plane, and once again, we shouldn't be flying the plane; we're letting someone else do that. We have our physics instruments out, and we're trying to measure the velocities of these other things from my frame of reference.

Well, the plane, first of all, is going to appear to be stationary, and that might seem counterintuitive, but if you've ever sat in a plane, especially when there's no turbulence and the plane is already at altitude and it's not taking off or landing, oftentimes if you close your eyes, you don't know if you are moving. In fact, if you close all the windows, it feels like you are in a stationary object; you might as well be in a house.

So from the plane's point of view, or from your point of view in the plane, it feels like the plane is stationary. Now, the ground, however, looks like it's moving quite quickly. It looks—it'll look like it's moving past you at 250 m/s. Whoops, trying to draw a straight line at 250. Sometimes my tools act funny.

So at 250 m/s to the left. And the car? Well, it's moving to the left even faster; it's going to be moving to the left 50 m/second faster than the ground is. So the car is going to look not like it's just going 50 m/s; it's going to look like it's going 50 m plus another 250 m/s for a total of 300 m/s to the left.

So this gives you an appreciation for what frames of references are; that you can view it for this introductory video as a point of view from which you're making your measurements. Now, it's tempting for a lot of folks to say, "Well, there must be one correct frame of reference." In a lot of times in our everyday world, you might say, "Well, maybe this is the correct frame of reference, and we're just imagining this, or this is just a mistake."

The reason why we do that is because we're using the frame of reference of this big giant thing called the Earth. But it actually turns out that none of these frames of reference are more valid than the other ones. They are all equivalent. They are all valid frames of reference.

Not—I shouldn't say they're equivalent; we're obviously getting different measurements from them, but they're all, physically, they're all, from a physics point of view, equally valid frames of reference.