# Proportionality

by Jared Rovny
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00:00 The next mindset that we’d like to discuss is proportionality. To be able to think about physical variables in terms of simple proportions. So for example one thing we’ll discuss is how far something is following if we drop it in a given amount of time. And if I ask you whether the distance that this thing has fallen depending on the time or the time squared, one thing that you might be able to find out using our unit analysis is that as we saw depends on time squared.

00:26 But supposed you have that as a given and I ask you a new question. So I say that first we drop it and we allow it to fall for a certain amount of time. But now we drop it and we allow it to fall for a new amount of time. Originally, it falls by some constant times, the time’s squared as we saw.

00:42 So it depends on with proportional to the time that you’re allowed to fall squared. But now I ask you a question and say what happens if I say double that time, I let it fall for twice as long, what happens to the new distance that it falls because I allow it to fall for a longer period of time.

00:59 What we can do is write the new falling distance in terms of the old falling distance because instead of writing constant times, the new falling time, I can write constant times twice the original falling time because we’ve said that the new falling time is twice the original time.

01:13 Putting in this factor of two and seeing that this whole quantity is going to be squared, we can just do the squaring, we can square the 2. 2 square is 4, so we can just factor out the 4 after doing this and then we get to the one tricky part which is up the entire thing to the right of the 4 that you see here is a constant times the original falling time squared. And that’s just your original falling distance that we see in the first line. So now we can see that the new distance that it fell is in fact just four times the original distance that it fell. So one way to just restate everything that we’ve just discussed here in a quick and simple way is if I allow something to fall for twice as long, it will fall 4 times as far. Understanding proportionalities like the distance falling depends on the times squared means that this is something that you would know very quickly just by thinking in your head If I double the time, what do I do to the distance if the distance depends on the time squared.

02:05 and so if I multiply the time by 2, the distance multiply by 4. If I for example multiply the time by 3, the distance would increase by 9. Because we will take 3 square and find 9 using the same method.

02:20 In this overview, we’ve discussed a basic idea what the course is going to look like as we go through and then there’s some skills that you'll want to know for the future. We reviewed scientific notations, which I highly recommend you practice often. We reviewed unit analysis and how to think about the units of variables in order to come to conclusions very quickly and easily. We also talked about how to think about variables simply in terms of what they're proportional to. Whether they’re proportional to a thing, or that thing squared, or that thing cubed and how to find new variables, new values based on the original values of variables very quickly and easily.

The lecture Proportionality by Jared Rovny is from the course Methods and Common Calculations.

### Included Quiz Questions

1. a'=a/16
2. a'=a/8
3. a'=a/4
4. a'=16a
5. a'=8a
1. a is quartered
2. a is halved
3. a remains unchanged
4. a is doubled
1. Value of ‘c’ will be quadrupled and value of ‘b’ will be quartered.
2. Value of ‘b’ will be quadrupled and value of ‘c’ will be quartered.
3. Value of both ‘c’ and ‘b’ will be quadrupled.
4. Value of both ‘c’ and ‘b’ will be quartered.
5. Value of both ‘c’ and ‘b’ will be squared.
1. 4 times.
2. 9 times.
3. 2 times.
4. For the same amount of time.
5. Half times.
1. Cubed
2. Doubled.
3. Change by 9 times.
4. Remain unchanged.
5. Changed by 18 times.

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Perfect Intro Setup to For Success in Physics
By Anthony M. on 04. August 2017 for Proportionality

Great lecture topic. Great setup to the course. This kind of math stuff (and its application) is key in Physics (and Gen Chem). My actual class would have been so much easier and more insightful if I was better versed in this stuff!