 To begin here, what I would like you to do is I would like you to make a short list, a list of three things that you can measure. But now that you've done that, I'm going to talk a little bit about what you wrote. What did you write? Maybe you wrote something like this. You might have said, I can measure weight. I get up in the morning, I get on my scale, I am measuring my weight. That might be an example of something you might have answered when I said, name something you can measure. Or you might have said, I can measure an apple. Now you probably didn't say that because most people wouldn't immediately think of measuring an apple, but that is a thing you can measure. Notice measuring the weight and measuring the apple, they both work with the word measure, but they're two different things. Or what you might have said is, I can measure time. Maybe that's how you answered the question. Okay, so there's a number of different ways we can kind of approach this, but let's see if we can reformulate that a little bit differently. So let's say we started with something like the apple as an example. I'm going to give this a term. I'm going to call it an entity. An entity being a thing. What is it that you measured? Something that you measured. You measured an entity, you measured an apple, you measured a wall, you measured a car. Or maybe you measured something between two places like the distance between Raleigh, North Carolina and Tilton, New Hampshire. So that's an entity. The other things we have listed here, the weight or the time are examples of quantities. So what I would like you to do now while I race the board is I want you to rewrite the three things that you have here in the terms of quantity of entity. For example, the weight of an apple. Were you successful? So, okay. So now that we're thinking about each of these things as entities and quantities, we measure something, a quantity, about something, an entity. When we do so, there are two other parts to our measurement that we think about. One of the things is when we say quantity and entity, we're gonna come up with a value. For example, the weight of an apple might be seven. Seven, seven what? Well, we also would need a next thing called units. We would need a scale whereby we would compare our measurements. So the weight of our apple might be seven ounces. For example, so come up with some examples for the three things that you said to measure. See if you can make up a value and some appropriate units. Notice the value in units tend to go together because the weight of the apple might also be half a pound. Well, maybe not seven ounces, but the idea is there's some relationship in between those two things where we could do something along those lines. So consider it that way. My example might be the height of basketball player LeBron James is 81 inches. So now that we've laid out these pieces of talking about things that we measure, now we're gonna talk about one of the things we do in science, where what we've done is we've looked at all the different things that we can measure and all the different ways that we can measure them, the different quantities that we can measure about the things that are in the universe. And in doing so, we discovered that there was lots of things that you could combine together that you could find relationships between. For example, we started thinking about this concept of speed, which is the relationship between how far something is moving and the time it takes. So speed is a distance and a time. It's a relationship between two other quantities. And in doing so, we decided, okay, let's look a little more carefully and we're going to divide our quantities into two types. One type are fundamental quantities and one type are derived quantities. Fundamental quantities are quantities that are fundamentally different from one another and that we can't necessarily combine other things together to get. We decided those are sort of our building blocks of discussing quantities. And there are a list of seven of these that we typically use. Now sometimes I make the mistake and I use the term fundamental unit or fundamental quantity interchangeably. We got to remember that quantities are the things like the weight, whereas units are the scale or the measure that we're using there. For example, ounces or pounds as weights. So let's go ahead and list some of the fundamental quantities. The first in our fundamental quantities we've already discussed here. The first and most standard one is time. That is a fundamental quantity. And we have units that are associated with that fundamental quantity and the standard unit for time that we use is the second. Pretty straightforward. Now there's another measurement that we use that's pretty standard. If we want to talk about measuring an apple we could talk about the height or the size of the apple measured in different ways. Well, the simplest measurement for size is something called length. And we also have interchangeable terms width or height which kind of talk about the direction that we're talking about, okay? But the quantity length is a very standard length. And you can see how length is very different from time. We measure them very differently. Now it turns out there are two systems whereby we measure things. One of these systems is an older system that was developed before we knew as much about science or before we defined things the same way as we do in modern times. And that was often called the imperial system or is now sort of the remnants of our leftover in what's called the US customary system. The system is relatively obsolete except in the United States and a few other places around the world. But this system, the US customary system we would often measure length in units called feet which is roughly the size of a human foot. Broken down into inches or miles which is 5,280 feet. But that's sort of a standard unit. It's still a fundamental unit that goes along with the fundamental quantity of length. We also have since developed another system, the system international or the metric system that we use that's based on different assumptions. And in this case, the standard unit of length is the meter which is something a little under three feet and there's a relationship there but we've measured a meter and generally we've based that meter on a standard based on some division of the size of the earth. And this system is used more commonly throughout the world. So we're gonna have to remember these two systems, the metric system, SI or System Internationale and then our US customary system, the system that is still being used in the United States. So time and length are pretty common. We already mentioned another one, we said weight. However, over time in history we discovered that even though we measured weight first we knew how to measure or quantify this idea of weight, how it felt when something was being pulled toward the earth and we tried to lift it. And that concept of weight we used as a unit for a long time and then eventually we learned that it was different, it was related to the amount of stuff that was in something, a concept called mass, the amount of stuff that we had in something. But for the longest time we used weight and it turns out that our fundamental unit that is typically used in the US system is a weight in terms of pounds. The fundamental unit of weight is a pound and very typically what we consider to be the fundamental unit when we're dealing with the US system is the pound. Well, that's kind of confusing, why would it be different? Again, some history involved there. The fundamental unit that we use for the metric system goes along with the fundamental quantity of mass and that is typically the gram or the kilogram. And this is where it can often get confusing when you're first learning the difference between mass and weight is the fact that the two systems tend to build differently. That we consider mass to be fundamental when we're dealing with the system international and we consider weight to be fundamental more typically when we're dealing with the US customary system. So now these three fundamental quantities are the ones that are primarily used early on in your study of physics. Okay, they're usually used in what's considered called mechanics, the study of mechanics and these are the basic ones that get used the most. As you move further into physics, you will encounter four more of them, physics and chemistry, that you'll encounter four more of them that are used fairly often and are still considered fundamental quantities. So I will give them and the unit associated with them but notice the unit associated with them is generally units associated with the system international because they are relatively more recent in our studies of science and therefore are established around the same time or after we really set the fundamental quantities and we set up the system international. So let me look at those. The first one is one that is actually more common in use than the others is temperature. Now if you think carefully about temperature, can you describe temperature in terms of time and length and mass? No, it's sort of fundamentally different. It's a different sort of phenomenon to describe. So we describe temperature in degrees Kelvin or degrees Celsius. Those are two common units in the system international and there are also scales in the US customary system. The common one is degrees Fahrenheit with which we can exchange with another one called degrees Rankine. So these are also considered fundamental units that go along with the fundamental quantity of temperature and in different systems. Another one is used commonly is quantity of material. This one's a little strange but basically it means account. If we are able to take things that have single units and count them up, one, two, three, four, five. We often use a term like that, for example, a dozen. A dozen is an example of a measure of a quantity of material that represents units of something that have been counted up. The thing that we count up more frequently in science or that we need this unit for is the number of atoms or the number of molecules that are in a certain amount of material. And so the common unit that we're using for that is something called a mole. But again, that's generally meaning a mole is 6.02 times 10 to the 23rd somethings. It's just a number associated with individual units. So it's kind of strange, a little bit different than those things but notice counting a number of entities is different than counting the time associated with a particular thing or entity. All right, two more to list here. One of them is going to be current, a representation of the amount of electricity flowing through a system. And typically that is measured in amperes. And then the last one on this list is luminous intensity, which is the measure of effectively sort of the brightness, the amount of light that is being exuded from something. And that has a measurement known as the candela relative to sort of a measurement associated with the amount of light a standard candle might emit. All right, so we have this list of fundamental units. All of these things are different from each other. Here's the units and here's the quantities associated with them. Well now that leads us to another category. Our other category is what are called derived units. What are derived units do you ask? Well, you can probably think of some things that are not on this list. See if you can think of something that's not on this list. Now, if you did, there's a good chance that what you chose can be made out of some combinations of things on this list. For example, a good common one is area. If I was trying to figure out how much paint I would need to paint a wall, for example, I couldn't just measure the length of the wall. I would also have to measure the height of a wall. So area is an example of a derived quantity. And we would get that by taking two lengths or a length times a width, multiplying them together. And once we multiply them together, we get something that might be measured in something like meters squared. A square meter would be an example of a derived unit. And we can tell it's derived because it's two fundamental units multiplied together. Sometimes we might even have other names for area that don't look like a derived unit, something like an acre. An acre is a measurement of area. However, it doesn't have some squared piece to it. It basically is an area. However, it is still considered a unit that goes along with a derived quantity. Similarly, volume. Volume is a three-dimensional version where we would have length times width times height. Or if you were trying to find the volume of a cylinder, it might be a more involved formula, pi r squared times height. And we would find out that that might be measured in something like meters cubed. Or we could rename that to be something like liters or milliliters as examples of units that go along with derived quantities. So those are pretty straightforward multiplications. We already mentioned another one. Speed, how fast something is moving. Notice that would be distance divided by time. And distance would just be an example, another name of a length instead of the length being the end to end of an entity is the length between two entities. But speed would be distance divided by time, which be measured in something like meters per second. One of our fundamental units divided by another fundamental unit. And you can continue to build up things as you see relationships in the universe. F equals MA. Well, we take mass and multiply it by acceleration. Well, acceleration, let's see here, F is force. And we know that force is mass times acceleration. And acceleration is a velocity divided by a time. And a velocity is a distance divided by a time. So if we take a mass times a distance divided by a time divided by a time, a mass times a distance divided by a time divided by another time, we get a big conglomeration of units that we've derived from multiplying and dividing from our fundamental quantities. And so force is a derived quantity. Now, some of you who are very savvy might be noticing that weight is a type of force. And that's true. If you decide to use the US system and use weight as your fundamental quantity, then we would be able to sort of say, okay, force is fundamental, but then we would have to work backwards and derive mass by doing things like multiplying it by acceleration. I mean by, sorry, by dividing the force by acceleration, and then we could find it that way. That makes it a little more confusing, and that's why many more people try to stay within the system international. Or sometimes we sort of gravitated a little bit to moving away from to trying to use mass sometimes in the US customary system, but that tends to be a little bit more complex. Other ones come into place, pressure. Pressure is a weight or a force divided by an area. Well, we can, over time, we can take the force, kilogram meters per second squared, divided by the area, divided by meters squared. So you have kilogram meters per second squared, divided by meters squared, maybe we cancel out, and we get something that looks like kilograms per meter second squared. It might be hard conceptually to think about what a kilogram per meter per second squared is, but the idea here is that all the pieces are things that we can figure out and measure from fundamental quantities. So hopefully this illuminated for you a little bit of the difference between our definitions of fundamental quantities and the associated units, and derived quantities, and the units that are generated from them.