Anderson Video - Unit Conversion

Professor Anderson
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>> There's a lot going on in physics, of course. And one of the things that you need to be very comfortable with is this idea of units and unit conversion. So, let's spend just a little time talking about units. Okay, if I give you a number, say 55, that might not mean very much to you. But if I said, "55 miles per hour," now that means a little more to you. So, units are the way of sort of quantifying the numbers that we're talking about. If I said, "55 centimeters per hour," that's a very different meaning to you than something like 55 miles per hour. So, in physics we use the international standard of units, SI units. Those are, of course, the kilogram, the meter and the second. And these units that you've heard of, but are maybe not totally familiar with and one reason you might not be so familiar with them is in the United States we use the English system of units. All right, so, let's talk about conversion, because we just mentioned 55 miles per hour, 55 miles per hour is, of course, a speed. How do we convert that -- -- to some other units? Well, it's very simple. All you have to do is multiply by 1. Okay, let's multiply by 1 every time. And let's ask the following question, let's say we have a person running. And they're running at 20 meters per second. How fast is that in miles per hour? And before we do that, let's ask this question, is this reasonable? Should they be able to run at 20 meters per second? Okay, so let's convert 20 meters per second to miles per hour. And what we said is all we have to do is multiply by 1 every time. So, what do we remember about, say, centimeters to inches? That's one thing that maybe we remember. And what remember is that 1 inch is 2.54 centimeters. This stuff here in parentheses is the number 1. 1 inch over 2.54 centimeters, that's the number 1, it's just in these funky units. All right, but that doesn't quite get us where we need, because we have to get centimeters out of there. So we remember that there's 100 centimeters per meter. Okay. Then what are we left with? Well, we can cross out the meters, we can cross out the centimeters and now we're left with inches and somehow we got to get inches into miles. So, we remember that there are 12 inches in 1 foot. And maybe you remember there 5280 feet in a mile. So, inches, crosses out with inches. Feet crosses out with feet. And we're left with miles. So, we've got 20 times 100 divided by 2.54 times 12 times 5280. We are in miles per second. All right, that's good. Now we got to get rid of seconds. So, 60 seconds in a minute, 60 minutes in an hour. Okay, every time you multiply by 1 you can take this number 1 and flip it the other way. Which one do you put on top and which one do you put on bottom? It's to cancel out the units appropriately. Okay, so any time you have something in the denominator you can cross out the corresponding units in the numerator. Minutes in the denominator crosses out with minutes in the numerator and now we're left with hours. And we have some numbers to multiply here. We got 20 times 100, times 60, times 60 and we're going to divide by 2.54 times 12 times 5280 and we're going to end up with miles per hour. And now we can multiply this stuff out. So, when you are multiplying out big numbers like this you can always approximate it on paper and I encourage you to do this, because it's good practice. So, 20 is 2 times 10 to the 1. 100 is 10 to the 2. 60 is 6 times 10 to the 1. And we have another 1, 6 times 10 to the 1. And then we are going to divide by 2.54 times 12, which is 1.2. Times 10 to the 1. 5280, which is 5.3 times 10 to the 3. And we should be able to multiply all those numbers and while I'm doing this, maybe you guys can plug it into your calculator and just see what you get. All right, so we got a 2 times a 6, which is 12. And 12 times 6 is -- what's 12 times 6? 72. And then we've got a 10 to the 1. We're going to add another 2 there, another 1 there, another 1 there, so we just count up the zeroes. 1, 2, 3, 4, 5. 72 times 10 to the 5 upstairs. Downstairs what do we have? Well, we've got 2 and a 1/2 times 1.2 times 5.3, that maybe is a little hard to do in your head, but let's just approximate. Let's say this is a 3, this is a 1 and this is a 5. So, that would be 15. And we have a 10 to the 3 down there. Okay. And, so, now we've got 72 over 15 or 72 times 10 to the 5 over a 150 times 10 to the 2. And that is approximately what? Well, that's a little bit less than a half. Right? So, let's say it's around 0.45. And then we have 10 to the 3 and that is 4. We move it over 3 spots, so we get 1, 2, 3 and we should end up with around 45 miles per hour. Did we do that right? >> This we did wrong right here, right? >> Yeah. >> Came out with the right answer, but the sig fig is off. >> What did you guys get when you plugged it in your calculator? >> 44.74. >> 44.74 miles per hour. But this last step here I think we messed something up. >> It should be 15 times 10 to the 4. >> You forgot like the 10 to the 1, you didn't at the bottom. >> You tell me. >> This one, right there? >> Yeah. >> That one right there. So this is actually 10 to the 3. And this 10 to the 2. Good. Now we're good. Everybody agree with that? >> Yeah. >>All right, so, 44 miles per hour. Can you run at 44 miles per hour? No, I mean, that would be like running down the road next to the cars and just cruising along, that's way too fast. So, your intuition was right. 20 meters per second is probably too fast for somebody to run. And the idea is that if you don't know exactly the units you're dealing with, if they make sense or not, those numbers, put them into units that do make sense to you and see. Okay. And let's come up with a way to remember this. 20 went to about 44, so let's approximate this. 1 meter per second is approximately 2 miles per hour. Okay, so if you are running at 20 meters per second it's approximately 40 miles per hour. Okay. Just double it. And this will help you make sense of the answers that you get on your homework problems. [ Music ]
>> There's a lot going on in physics, of course. And one of the things that you need to be very comfortable with is this idea of units and unit conversion. So, let's spend just a little time talking about units. Okay, if I give you a number, say 55, that might not mean very much to you. But if I said, "55 miles per hour," now that means a little more to you. So, units are the way of sort of quantifying the numbers that we're talking about. If I said, "55 centimeters per hour," that's a very different meaning to you than something like 55 miles per hour. So, in physics we use the international standard of units, SI units. Those are, of course, the kilogram, the meter and the second. And these units that you've heard of, but are maybe not totally familiar with and one reason you might not be so familiar with them is in the United States we use the English system of units. All right, so, let's talk about conversion, because we just mentioned 55 miles per hour, 55 miles per hour is, of course, a speed. How do we convert that -- -- to some other units? Well, it's very simple. All you have to do is multiply by 1. Okay, let's multiply by 1 every time. And let's ask the following question, let's say we have a person running. And they're running at 20 meters per second. How fast is that in miles per hour? And before we do that, let's ask this question, is this reasonable? Should they be able to run at 20 meters per second? Okay, so let's convert 20 meters per second to miles per hour. And what we said is all we have to do is multiply by 1 every time. So, what do we remember about, say, centimeters to inches? That's one thing that maybe we remember. And what remember is that 1 inch is 2.54 centimeters. This stuff here in parentheses is the number 1. 1 inch over 2.54 centimeters, that's the number 1, it's just in these funky units. All right, but that doesn't quite get us where we need, because we have to get centimeters out of there. So we remember that there's 100 centimeters per meter. Okay. Then what are we left with? Well, we can cross out the meters, we can cross out the centimeters and now we're left with inches and somehow we got to get inches into miles. So, we remember that there are 12 inches in 1 foot. And maybe you remember there 5280 feet in a mile. So, inches, crosses out with inches. Feet crosses out with feet. And we're left with miles. So, we've got 20 times 100 divided by 2.54 times 12 times 5280. We are in miles per second. All right, that's good. Now we got to get rid of seconds. So, 60 seconds in a minute, 60 minutes in an hour. Okay, every time you multiply by 1 you can take this number 1 and flip it the other way. Which one do you put on top and which one do you put on bottom? It's to cancel out the units appropriately. Okay, so any time you have something in the denominator you can cross out the corresponding units in the numerator. Minutes in the denominator crosses out with minutes in the numerator and now we're left with hours. And we have some numbers to multiply here. We got 20 times 100, times 60, times 60 and we're going to divide by 2.54 times 12 times 5280 and we're going to end up with miles per hour. And now we can multiply this stuff out. So, when you are multiplying out big numbers like this you can always approximate it on paper and I encourage you to do this, because it's good practice. So, 20 is 2 times 10 to the 1. 100 is 10 to the 2. 60 is 6 times 10 to the 1. And we have another 1, 6 times 10 to the 1. And then we are going to divide by 2.54 times 12, which is 1.2. Times 10 to the 1. 5280, which is 5.3 times 10 to the 3. And we should be able to multiply all those numbers and while I'm doing this, maybe you guys can plug it into your calculator and just see what you get. All right, so we got a 2 times a 6, which is 12. And 12 times 6 is -- what's 12 times 6? 72. And then we've got a 10 to the 1. We're going to add another 2 there, another 1 there, another 1 there, so we just count up the zeroes. 1, 2, 3, 4, 5. 72 times 10 to the 5 upstairs. Downstairs what do we have? Well, we've got 2 and a 1/2 times 1.2 times 5.3, that maybe is a little hard to do in your head, but let's just approximate. Let's say this is a 3, this is a 1 and this is a 5. So, that would be 15. And we have a 10 to the 3 down there. Okay. And, so, now we've got 72 over 15 or 72 times 10 to the 5 over a 150 times 10 to the 2. And that is approximately what? Well, that's a little bit less than a half. Right? So, let's say it's around 0.45. And then we have 10 to the 3 and that is 4. We move it over 3 spots, so we get 1, 2, 3 and we should end up with around 45 miles per hour. Did we do that right? >> This we did wrong right here, right? >> Yeah. >> Came out with the right answer, but the sig fig is off. >> What did you guys get when you plugged it in your calculator? >> 44.74. >> 44.74 miles per hour. But this last step here I think we messed something up. >> It should be 15 times 10 to the 4. >> You forgot like the 10 to the 1, you didn't at the bottom. >> You tell me. >> This one, right there? >> Yeah. >> That one right there. So this is actually 10 to the 3. And this 10 to the 2. Good. Now we're good. Everybody agree with that? >> Yeah. >>All right, so, 44 miles per hour. Can you run at 44 miles per hour? No, I mean, that would be like running down the road next to the cars and just cruising along, that's way too fast. So, your intuition was right. 20 meters per second is probably too fast for somebody to run. And the idea is that if you don't know exactly the units you're dealing with, if they make sense or not, those numbers, put them into units that do make sense to you and see. Okay. And let's come up with a way to remember this. 20 went to about 44, so let's approximate this. 1 meter per second is approximately 2 miles per hour. Okay, so if you are running at 20 meters per second it's approximately 40 miles per hour. Okay. Just double it. And this will help you make sense of the answers that you get on your homework problems. [ Music ]