Frames of reference | Movement and forces | Middle school physics | Khan Academy

When we make new discoveries, we need to be able to share them with others. The first thing we have to do is make sure everyone is on the same page. We do this by using units and frames of reference, which are also called reference frames. We talk about units in another video, so let's look at what a frame of reference is.

Let's say this blue box thing is a car, and it's going 45 miles per hour. Someone standing on the side of the road would see it pass at 45 miles per hour. Now, if this yellow truck is going 40 miles per hour, someone sitting in the yellow truck would observe the blue car traveling at 5 miles per hour. How could the person on the side of the road see the blue car traveling at 45 miles per hour, and a person in the yellow truck see the blue car moving at 5 miles per hour? This is because both observers are using different frames of reference.

So, let's go ahead and take a look at that, starting with the speed of the blue car. The person on the side of the road is using their frame of reference of being at rest, so relative to them, the blue car is moving at 45 miles per hour. To the person in this yellow truck, which remember is already going 40 miles per hour, the blue car is going 5 miles per hour.

Now, let's do the exact same thing for the speed of the yellow truck. So, what is the speed of the yellow truck for the observer on the side of the road? It's 40 miles per hour. And what do you think the speed of the truck is for the person using their blue car as the reference frame? Well, the blue car is moving at 45 miles per hour, and the truck is only moving at 40 miles per hour.

So, the speed of the yellow truck is actually five miles per hour slower than this reference frame because the blue car is already moving at 45 miles per hour. Now, you might be thinking, "But wait, the person on the side of the road isn't really at rest; they're on the earth, and the earth is moving!" You're completely correct. The person is at rest with respect to the earth.

The earth is the most common frame of reference that we use. To an observer in space who is not rotating with the earth, the blue car is going 45 miles per hour plus the speed of earth's rotation. This is why frame of reference is so important. We just talked about one blue car having three different velocities depending on what the frame of reference is.

How would we communicate this to avoid confusion? Well, we state the reference frame we're using: "The blue car is moving at five miles per hour with respect to," which I'll write as "wrt," "the yellow truck." This tells us that the yellow truck is our frame of reference. Or we could say that "the yellow truck is moving at 40 miles per hour, and the blue car at 45 miles per hour with respect to the earth." That way, everyone is on the same page—a page which, to be clear, isn't a book that relative to me is at rest.