Reference Frame

Reference Frame

The first thing to focus on when studying motion of an object or person is their position. The word position describes your location (where you are). However, saying that you are here or there is meaningless, you have to use known points (reference points) to help specify your position.

For example, if you were in a classroom and wanted to tell a classmate where you were standing you would first give them a reference point. The reference point might be the classroom door. You would then be able to say that you are \(\text{2}\) \(\text{m}\) from the doorway. This still doesn't give your position precisely. We need to provide a reference point and a coordinate system to use to define the location precisely.

Describing Your Location

Then you can say that you are, for example, \(\text{2}\) \(\text{m}\) from the door directly inside the classroom. The classroom door is a reference point and inside/outside is the coordinate system you have chosen. A frame of reference or reference frame is reference point which serves as the origin for a coordinate system. The coordinate system can be up or down, inside or outside, left or right or even forward or backward. These are all examples that define a \(\text{1}\)-dimensional coordinate system. We choose one of the directions as the positive direction.

A graphical representation of a \(\text{1}\)-dimensional frame of reference:

Frame of Reference

You can define different frames of reference for the same problem but the outcome, the physical results, will be the same. For example, a boy is standing still inside a train as it pulls out of a station. Both you and the boy define your location as the point of reference and the direction train is moving as a where you are standing as the point of reference and the direction the train is moving in as forward.

You are standing on the platform watching the train move from left to right. To you it looks as if the boy is moving from left to right, because relative to where you are standing (the platform), he is moving. According to the boy, and his frame of reference (the train), he is not moving.

A frame of reference must have an origin (where you are standing on the platform) and at least a positive direction. The train was moving from left to right, making to your right positive and to your left negative. If someone else was looking at the same boy, his frame of reference will be different. For example, if he was standing on the other side of the platform, the boy will be moving from right to left.

For this chapter, we will only use frames of reference in the \(x\)-direction. By doing this we restrict ourselves to one dimensional motion. We can use the sign of the position value (positive or negative) to indicate the direction relative to the origin.

For example the blue dot in the figure below can only move along the \(x\)-axis.