## Tuesday, August 24, 2021

### Frame of Reference

Introduction to Chemistry and Physics Index

Physics Index

Where are we going with this? The information on this page introduces the broad topic of physics by identifying different fields within it.

Frame of Reference
(You're just making things up, now, aren't you?)

Frame of reference seems like… like… I don't know what it seems like.

The purpose of having a frame of reference is to create a system (often using X, Y, and Z axes1) in which numeric values can be associated with the positions of and motion of the things within the system. Both the space and the objects within the space are related by means of the frame of reference.

1 The plural of axis is axes.

When creating a frame of reference, the end goal is to make the math easier and to make describing what's going on more clear.

And… a definition on this one is going to be… fuzzy.

Perhaps it is best to define by examples?

SITUATION 1

Think of a ball rolling. Now, think in two dimensions. Okay, NOW think of the ball rolling from the left to the right. OKAY NOW… here's the cool part!

So, we have a ball moving in 2 dimensions. Moving… that implies positions. And directions. So…

When establishing the frame of reference for this situation, you get to decide some things… Like:

What quantities are we using to measure things? (distance, length, relative position…)
What are some units that go with those quantities?

Where is zero?
Which direction is bigger than zero (positive)?
Which direction is negative?

You can decide.

Let's say left is negative and right is positive.

So, if the ball is at 4 on the meter stick and it moves -2 centimeters, then it moved left.

And, if it moves right 6 cm, then it moved +4 centimeters?

Thus… left is negative and right is positive.

SITUATION 2

Think of a ball rolling. Now, think in two dimensions. Okay, NOW think of the ball rolling FROM some place TO some other place.

Perhaps in this frame of reference, away from the origin is positive. As it moves away the measure of position increases.

It started 2 meters away from a reference point. It moved further away by 2 meters. The distance from the reference point would be greater.

If it started 2 meters away and moved toward the reference point by 1 meter, the distance from the reference point would be less.

SITUATION 3

Up and down…

This is interesting to think about because, sometimes in order to make the math easier, up needs to be positive and down needs to be negative. Other times (say you want to know how far something falls) down is better as the positive and up negative.

SITUATION 4

To infinity and beyond!

Say you have two satellites, one following the other. At different velocities relative to a planet.

If the question asks about something involving only the two satellites, it might be easier to develop a frame of reference wherein one of the satellites is considered the origin and only the relative motion between the two is factored in.

SUMMARY

A good frame of reference…

… make the math easier.

… allows clear communication of what's going on.

… is specific to a given situation.

Different frames of reference can exist for the same situation, so understanding how to interpret them is important.