AP Physics Chapter 1 Study Guide

Concepts of Motion and Mathematical Background

Welcome to the AP Physics Chapter 1 Study Guide. This chapter is an introduction to the study of motion and some background knowledge of mathematics.

Motion Diagrams

There are four main types of motion that will be covered in this class. Straight-line motion, projectile motion, circular motion, and rotational motion.

Straight-line Motion Projectile Motion Circular Motion Rotational Motion Combination
Straight line Motion
Projectile Motion
Circular Motion
Rotational Motion
Combination

 

Creating a Motion Diagram

This is four frames from a movie. The time between frames is constant. For example, most television is filmed in 30 frames per second. So the time between frames is 1/30 th of a second.

Figure 1-2

However this would be tedious to use film for motion diagrams. So if we make a motion diagram pictured below, that would be easier. It is emphasised that the time between images is a constant.

Figure 1-3

If you are anything like me in drawing this would also be to tedious. So what we do is think of the cars as a particle, or point. This is usually the center of mass of the object. The motion diagram now looks like the image below.

Motion Diagram 1

 

Some other motion diagrams to discuss. Draw a particle motion diagram for each of the following diagrams.

motion 1

 

motion2

 

motion 3

 

motion 4

 

motion 5

 

 

Which car is going faster, A or B?

Stop to think

 

Give an example of a object that could be moving for each of the following motion diagrams.

stop to think

 

Position and Time

position

We need to have an easier way of finding position than the above diagram.

 

position

 

But, will this work for another situation.

position

 

Then on a none flat surface the situation changes.

position

 

But, how does time come into play for the motion diagrams?

 

Instead of putting just numbers on the motion diagrams we could put time in seconds or minutes or any other time appropriate to the situation.

position time

Describe a situtation that the above motion diagram shows.

 

position time

 

Displacement

Displacement is the change in position of an object, calculated by taking the final position minus the initial position.

displacement

To find the displacement above you take the final position (150 ft) then subtract the initial position (50 ft) from the final to get a displacement of 100 ft.

 

displacement

This displacement will be negative, because 0 ft minus 50 ft is a negative 50 ft.

 

Velocity

Speed is a the rate of motion, or equivalently the rate of change in position, often expressed as distance d traveled per unit of time t. Speed is a scalar, because it has no direction.

 

speed

 

speed

 

Velocity is defined as the rate of change of displacement. It is a vector quantity; both speed and direction are required to define velocity.

 

velocity

 

velocity

 

 

Significant Digits

significant digits

 

Operations with Significant Digits

operations

 

Rounding

rounding

 

SI Units

Factor
Prefix
Symbol
Figure
yotta-
Y
Figure
zetta-
Z
Figure
exa-
E
Figure
peta-
P
Figure
tera-
T
Figure
giga-
G
Figure
mega-
M
Figure
kilo-
k
FIgure
hecto-
h
Figure
deka-
da
Figure
deci-
d
Figure
centi-
c
Figure
milli-
m
Figure
micro-
µ
Figure
nano-
n
Figure
pico-
p
Figure
femto-
f
Figure
atto-
a
Figure
zepto-
z
Figure
yocto-
y

 

Vectors

Scalar is a physical quantity that has magnitude but no direction.

Vector is a physical quantity that has both magnitude and a direction.

vector

 

Vector Addition - when you add vectors you must use trigonometry and triangles to add the vectors.

vector addition

 

Sample Vector Practice in Class

 

Pictoral representation of vectors.

vectors

 

An example of the velocity of a ball thrown in the air.

ball diagram

 

Modeling in Physics

data graph

 

Linear graph

 

slope

 

parabola

 

inverse