Unit 1 Breakdown
You are on Lesson 1 of 5
- Unit 1.1 | Understanding vectors and the standard units used in Physics [Current lesson]
- Unit 1.2 The kinematic (motion) variables: Displacement, velocity, and acceleration
- Unit 1.3 | Graphing motion
- Unit 1.4 | Using kinematic equations in 1 dimension
- Unit 1.5 | Projectile motion: Using kinematic equations in 2 dimensions
In this lesson you will learn:
- Kinematics – What it is?
- Vectors – what they are and how/why we use them in Physics
- Vector manipulation – adding and splitting up vectors
- Units – motion graphs and equations
Introduction
Hello, young physicists! Welcome to the exciting world of physics. We will embark on a journey to understand the universe and the principles that govern it.
Kinematics, or the study of motion, is the first part of this journey.
It makes up 12-18% of the AP Physics 1 content. Or around 10% of a regular Physics curriculum.
HOWEVER, in order to understand Kinematics and the rest of Physics we must cover 2 important topics first: Vectors and Standard Units.
After covering these topics in this first lesson, you will then officially begin your Physics journey!
What are vectors?
Vectors are simply arrows! This might seem boring, but vectors will be used EVERYWHERE in physics, not just kinematics. So it important to understand this well!
Vectors, or arrows, have two things: a length (also called a magnitude or scalar) and a direction.
Length and direction
The length can represent anything like distance, speed, forces, and more.
And the direction can be given as any of the 4 things below:
Vector example: riding on a bike at 5 m/s north. Notice how BOTH the magnitude (5 miles) AND the direction (north) is specified.
Vectors vs Scalars
| Scalar (just a number) | Vector (number and a direction) |
| volume (1 liter) | – |
| time (30 seconds) | acceleration due to gravity (-9.81 m/s2) |
| distance (10 feet) | displacement (10 feet north-west) |
| speed (100 km/hr) | velocity (100 km/hr south) |
| mass (25 kg) | force (15 Newtons, 30° above the horizontal) |
Why we use vectors
You might be wondering where and why we use vectors in physics.
Using vectors allows us to view motion in multiple directions.
Look at the image below. The soccer ball is kicked at a speed (v0) that is 30º above the soccer field.
Note that v0 is the variable for “initial velocity (speed).” It simply is a placeholder for the numerical value of the velocity of the soccer ball.
Physicists can take the v0 vector and separate it into two parts: the H vector and the R vector as shown in the image. These are what we call vector components.
In just a few minutes you, I’ll show you how to use simple trigonometry to find the components of a vector.
The result of breaking down a vector
Since we can break 1 vector down into 2 components of this motion, we can see that the ball is really moving both up and to the right at the same time.
We can use these components (or parts of the velocity vector) to solve real world problems, like how far did the ball travel before landing on the ground?
[LRN] Video – Vector math and finding components
In Physics, there are 4 things you will be doing with vectors. The most important one is the last one and there is a short video below showing how to do it.
- Take a vector and multiply it by a scalar.
- Doing this increases the size the of the vector.
- Take two vectors along the same axis and combine them to get a resultant vector.
- This is what we mean by adding and subtracting vectors
- Take two vectors the are perpendicular to each other and combine them to get a resultant vector.
- You will have to use pythagorean theorem to find the magnitude of the resultant vector
- Lastly, you can take 1 vector and break it down into two components.
- One horizontal component and one vertical component.
Okay now that you what we can do with vectors, lets put into practice! Watch the short video below, and try the example problems after.
PQ – Vector components
After watching the video above you should have a solid understanding of adding vectors and breaking them into components. Attempt all the practice questions below and be sure to understand all missed ones before moving on.
Find the resultant vector (magnitude AND direction) given the following components:
Find the X and Y components of the following vectors:
Challenge: Listed below are 4 distance vectors.
- A: 15 m at 60° above the +x-axis
- B: 10 m east
- C: 25 m south
- D: 50 meters at 28° South of West
Preform the following operations:
Hint: Draw out each vector on a graph. Break each vector into x and y components, then preform the operations in each direction.
Using the standard units of measurement
If you’re from the United States you may be used to seeing miles, miles per hour, feet, pounds etc.
This is the imperial system of measurement. And it makes calculations and conversions difficult.
Instead, in physics, we use the metric system (kilometers, meters, kilograms, etc) that the rest of the world is familiar with.
Why metric?
The metric system is much easier to convert between orders of magnitude.
For example, how many centimeters are in a meter? Well we can simply look at the prefix “centi” and tell that there are 100 centimeters in 1 meter.
So in Physics, you’ll commonly see the following standard units:
- Distance is measured in meters (m)
- Speed is measured in meters per second (m/s)
- Weight is measured in kilograms (kg)
- Time is measured in seconds (s)
From now on, when solving a problem, make sure to convert all give numbers to the standard units above!
Unit conversions
As mentioned earlier, converting units is pretty easy in the metic system.
You just have to memorize what each prefix means. The chart below will help with that.
As you do more Physics problems, unit conversions will become super easy!
AND ff you are having trouble converting units, watch this simple video explanation.
PQ – Converting units
Solve ALL problems before checking your answer below.
- Convert 320 grams to kg
- Convert 145 mm to meters
- Convert 100 km/hr the standard unit of velocity used in Physics
- Convert 50 cm/min to m/s
- Convert 365 days to seconds
- Given that 1 inch = 2.54 cm convert 4674 inches to meters
- The volume of a steel cube is 300 cm3. Convert this to m3
- The density of a iron sphere is 7.9 g/cm3. Convert this to kg/m3
Lesson 1.2 Preview
In the next lesson we will begin to cover kinematics by exploring the 3 kinematic variables: displacement, velocity, and acceleration. We will use standard units. In lesson 1.4 we will begin to utilize our knowledge of vectors to real world problems.
