In this lesson, we will examine scalars and vectors, learn why it is important to know the difference between the two and why remembering to add a direction to many of your exam answers could be the reason you get it right or wrong.
I just baked an apple pie. Would you like a piece? Let's make it a game. I'm going to put the pie on the table, blindfold you and give you directions to the pie. We'll see how fast you can find it. Ready? Walk 10 meters, then 5 meters, then 12 meters, then 5 meters.
Did you find the pie? No? That's impossible. I told you exactly how far you needed to walk. I'll give you another chance. Walk 10 meters north, then 5 meters west, then 12 meters south, then 5 meters east. Congratulations! Pretty tasty pie.
Believe it or not, this little test was a perfect example of the similarities and differences between scalar quantities and vector quantities in physics - and why you can't afford to mix the two up when attempting to solve a problem.
We'll begin by defining a scalar quantity. A scalar is any quantity that does not include a direction. In the first attempt of your pie challenge, 10 meters, 5 meters and 12 meters were scalars. All I provided you with were distances with no directions of travel. Without a direction, you had no idea which way you were supposed to start walking and no idea which way to turn. In this case, you needed more information.
Now you might be thinking that the scalars are missing something and should always have a direction added, but this isn't the case. There are many values in physics that only exist as scalars. These include speed, mass, electrical charge, energy and temperature. Let's look at temperature as an example. If I tell you it is 31 degrees Celsius outside, you know it is pretty warm. The number alone is enough to provide all the information you need. To take it a step further, there isn't even a way to logically put a direction on a temperature measurement.
Now let's look at vector quantities. A vector is any quantity that involves a magnitude and a direction. During your second attempt to find the pie, I added directions to the number of meters you needed to walk. Ten meters north, 5 meters west, 12 meters south and 5 meters east were all vectors. Ten, five, twelve and five are the magnitudes of the distances you needed to travel. North, south, east and west provided the direction of travel. In this case, you needed both pieces of information to solve the problem and find the pie.
You encounter many quantities in physics that are represented as vectors: acceleration, displacement, velocity and electric and magnetic fields. It's important to remember that you need both a magnitude (10 meters) and a direction (north) to fully represent the vector. Forgetting to add the direction can lead to you getting questions wrong, even if you calculate all the magnitudes correctly.
Let's briefly review scalars and vectors. A scalar is any quantity that does not include a direction. Measurements like temperature or speed do not need a direction to be correct and complete.
A vector is any quantity that involves a magnitude and a direction. Acceleration, velocity and displacement all require a magnitude (how fast, far or the rate) and a direction (north, south or any other directional term) to be considered correct.
Following this video lesson, you should be able to:
- Differentiate between scalar and vector quantities
- Provide examples of both types of quantities