Systems of Units

You’re going to use units with whatever engineering
calculations that you do, and it’s important that you keep them relative to your answer.
And what I mean by that is by not reporting things in certain units that don’t make sense. For instance, you wouldn’t want to measure
the volume or height or length of an elephant in centimeters, nor would you give the length
of a mouse in miles. Same thing with other units, so it’s important that we just kinda go through these, a little refresher on those. I have a table here for base units and base units are things that you would measure, you’d measure the length, mass, moles of something, these
are going to be, hence the word “base units”, what you’re going to do calculations with.
And so, I have this chart. Go ahead and see if you can pause and try to fill it in. Starting with length, the units of length can be reported in three different systems, we’ll talk about the SI, the cgs system, and the American engineering
system and you’re probably be most familiar with the SI system if you’ve worked with engineering
units before, or if you’re an American student, then you’ll probably be familiar with the
American engineering system. So when we talk about length, typically it’s
going to be in meters or centimeters or feet and feet also might be inches or yards. So we
abbreviate these–you never want to write these out in full–we abbreviate meters with
“m”, centimeters with “cm”, and then feet, inches, and yards. And of course, this is probably all stuff you know pretty well, so I’ll go quickly through this. So with mass, we’ll talk about grams. We will
also talk about pounds. These are “g” for grams and “lbs” for pounds, and we typically will put a subscript “m” after pounds to signify that it’s a mass–you can watch the other
screencast on “Weight vs. Force” just to get an idea of why in the American engineering
system, “pounds” can be “pounds mass” or “pounds force” depending on the units that you want. So with moles, you might have a gram-mole.
You might also just have a mole, or you could have a pound-mole. And those are kind of already
abbreviated… Time is pretty universal: a second and also,
of course, minutes, days, and et cetera. You could probably think of a couple other ones.
Abbreviations are “s”, or “min”. Temperature will typically be in either Kelvin
or Celsius. There’s also Fahrenheit or Rankine–abbreviated as degrees Celsius, Kelvin, degrees Rankine,
and degrees Fahrenheit. So Kelvin’s the only one that doesn’t have an actual degree sign. Electric current is in amperes, and that’s
signified with an “A”. Lastly, light intensity has base units of
candela, or “cd”. So as I mentioned before, it’s important that
we use the appropriate units in cases, so there’s what we call multiple units–and in
this case, it’d be nice to test yourself a little bit; see if you can fill in some of
these. When you think of “tera”, what does that mean? Well, a tera is basically a 10
to the 12th; you’re probably familiar with the term “terabyte”–and that would be that
there’s 10^12 bytes. So instead of writing it out as such, we can just say that it’s
one terabyte. Same thing with giga, a gigabyte is 10 to the 9th, so either 1 x 10^9 bytes, or just one gigabyte. “Mega” there’s other things you’ve probably heard of, A “mega-Watt” may be familiar. that’s 1 x 10^6. And you’re probably way more familiar with
the “kilo” term, because we see it in so many other places. It’s only 10 to the 3rd–for
instance you have 1 x 10^3 grams or one kilogram. You also see it in kilo-Watts, kilograms,
kilometers… When we start talking about the ones on the
right, instead of 10 to a positive number, they’re going to be the opposite: “centi”
is to the minus 2. Probably the most common thing we see is a centimeter. You might also
see a centigram or a centiliter. For a centimeter, you would have 1 x 10^(-2) meters, or just
one centimeter. “Milli” is 10 to the minus 3. Typically you’ll
see a millimeter, and you might also see a milligram. And we write this as 1 x 10^(-3)
meters, or you could rewrite it as one millimeter. And “micro” is 10 to the minus 6. You write it as micro-meter, maybe microgram, and microliter–and I also forgot milliliter up here, that’s a pretty common one, so again, if you wanted to write 7 x10^(-6) Liters, you could also just write 7 microliters typically that’s an easier way to record it and more relevant. And lastly is “nano”. You might think of a
nanogram, a nanometer. This is 10 to the minus 9. So, again, if you were
reporting 100 nanometers, you could write 100 x 10^(-9) meters, but it’s probably a
lot simpler just to write 100 nanometers. The last thing is what we consider to be “derived
units”. These are called derived units because they are based on our base units, some kind of multiple
or division of them. Volume is length cubed, and so what you see
for volume typically is a Liter, or you might also see a gallon. In American units, we talk
about cups, quarts, and so forth. In terms of base units, we could re-write a liter as
0.001 meters cubed, and we could also write it as 1,000 centimeters cubed. So just keep
in mind that a centimeter cubed is equivalent to one milliliter. When we talk about force, there’s the Newton
in the SI system, and there’s also the dyne. In the American system, you’ll see something known as pounds-force. Now, in terms of the base units, we know that a
force is just a mass times an acceleration. So for the base units, one Newton is equal to one kilogram mass times an acceleration, so meters per second squared. A dyne is just written as one gram centimeter
seconds squared, and a pound-force ends up being 32.174 pounds-mass feet per seconds
squared. Now, pressure is a force over an area. We
consider from the SI system what’s known as the Pascal. You might also be familiar with
atm and in the American engineering system, psi–and that is pounds per square
inch. In terms of their base units, since it’s a force per area, we’ll typically re-write
it as a Newton per meter squared–and that could simplify. I’ll leave that to your own
exercise. Then there are conversions between atm and Pascals and psi, and that’s something
you’ll have to look up in terms of conversion factors. Energy and work is just going to be a force
times a distance. So when you think about that, there’s a Joule, or erg, or a gram-calorie. So in terms of the base units, since it’s a force times a distance, a Joule would be one Newton-meter, and
again, that could simplify if you plug in what a Newton is. An erg is just one dyne-centimeter,
and then a calorie typically is related to Joules as such. And lastly, power is just an energy per time, so
one system of power you will see very often is a watt, which is SI and it’s written as a “W”. And
again, a nice thing about the SI system is that it’s simple to remember: a Watt is one
Joule per second. And again we can simplify, I’ll do this one for you, A Joule being a Newton-meter, a Newton being a kg-m/s^2, this would come out to be 1 kg-m^2/s^3. So again, become familiar with all three systems of units, even though SI is probably the most widely used it’s also one of the easiest to use, just because of the relationship between the units, you know, one Newton-meter being a joule, one Watt being
one joule per second, et cetera. The American Engineering system sometimes has hard to remember
conversions–for example, 12 inches in a foot, 3 feet to a yard, 5280 feet to a mile, that
kind of thing. It’s also important with this, just to keep
in mind the system that you’re looking at–you don’t want to report the power for a reactor
in microWatts, or kiloWatts that end up equaling that of the sun, it just doesn’t make a whole lot of sense. So again, remember to check your units at the end of every answer make sure that they
add up to the dimension that you’re looking for, and that they are appropriate for the
system you’re reporting.

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