Introduction

Welcome to the FiveHive article for Unit 1.4 of AP Physics 1! 

In this unit, we will be covering the frame of reference and relative motion. This will be explored by considering different perspectives and making observations about motion from each perspective.

As usual, we will only cover what is mentioned on the CED for Unit 1.4. 

Frame of Reference

To start, let’s define a frame of reference, or reference frame (these will be used interchangeably). A frame of reference is a system from which an observer measures position, velocity, acceleration, and other physical quantities of an object. In a way, it is the “viewpoint” from which one views the world. 

The values of the physical quantities that we will observe will change depending on how we set up our frame of reference. When observers use different reference frames, they will record different values for the same situation or see the same situation in different ways. Let’s consider the classic example of a ball being thrown straight up on a train moving in a straight line. 

In this scenario, we will have two different observers: one who throws the ball from inside the train and one who observes the ball being thrown from outside the train. To the person throwing the ball inside the train, it will seem as if the ball went straight up and came straight down. However, for the observer from outside, the ball will appear to have taken a parabolic path. 

This difference occurs because each reference frame will have its own coordinate system. In addition, the relative motion between the two reference frames will cause the observers to see different types of motion. In our case, the parabolic path and the vertical path. 

A Special Type of Reference Frame

The thing about reference frames is that they can often be moving in an unpredictable way. As a result, we often assign what is called an inertial frame of reference. This is a “special” type of reference frame that is not moving or is moving at a constant velocity. Meaning, this reference frame is not subject to acceleration. It is also often noted that in these frames of reference, Newton’s laws of motion work as intended. Additionally, the acceleration of all objects is the same as measured from all inertial reference frames.

Fun Fact:

In many cases, we assign the role of an inertial frame of reference to the Earth! This is extremely ideal, as the rotation of the Earth makes it not a truly inertial reference frame. But in the scope of this course, it is counted as an inertial reference frame. 

Maybe that fact wasn’t as fun as I intended it to be; nevertheless, it is an important fact. 

Relative Motion

For AP Physics 1, our exploration of relative motion will be restricted to one dimension. As a result, our addition of vectors in relative motion will also be restricted to one dimension. 

Converting Measurements Between Frames of Reference

We will analyze motion in different reference frames. As a result, we will need to use methods to convert measurements between them. To convert measurements between frames of reference, we need to determine the relative motion between the frames and use vector addition to make measurements. 

For instance, let’s consider you in a bus moving East at $200\text{ m/s}$ relative to the ground. We want to find out what your velocity with respect to the ground is if you decide to start walking towards the front of the bus at $1\text{ m/s}$. 

First, we establish the reference frames: 

Now, to find your velocity relative to the ground, we have to perform vector addition, which follows this equation:

${\mathbf{v}}_{\mathbf{A},\mathbf{C}}={\mathbf{v}}_{\mathbf{A},\mathbf{B}}+{\mathbf{v}}_{\mathbf{B},\mathbf{C}}$

In our situation, you are A, the bus is B, and the inertial reference frame(the ground)  is C. To find your velocity relative to the ground, we add the bus’ velocity relative to the ground and your velocity relative to the bus:

${\mathbf{v}}_{\mathbf{A},\mathbf{C}}=1\text{ m/s}+200\text{ m/s}$

$\therefore {\mathbf{v}}_{\mathbf{A},\mathbf{C}}=201\frac{\mathrm{m}}{\mathrm{s}}$

NOTE:

It is important to understand and remember that velocity changes with a difference in reference frame. This may seem obvious, but under a time crunch, it is these small details that are prone to being forgotten. 

Another Note:

Unless specified by the question, a reference frame is always assumed to be inertial. 

Practice:

Congratulations! You have survived yet another AP Physics 1 topic. Nice work! 

Now, it is time to lock in your understanding with some practice questions.