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Circumference, Period, and Frequency in UCM

Patrick Ford
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Hey, guys. So now that we've been introduced to uniform circular motion in this video, we're gonna talk about three more important variables. You'll need to know circumference, period and frequency. So let's go ahead and check it out. Basically, they are all related to when objects complete a full rotation. So we have these circular path, and once you complete a full lap around this circle, you've completed a full rotation. Some books will call this a revolution, and some will call it a cycle. So let's talk about the first one, which is basically the distance that you travel around the circular path that's called the Circumference. The circumference is given by the letter C, and it's really just related to the radius. We know that the radius this is really just the distance from the edge of the path to the center of the circle that are the circumference is basically going to be the distance all the way around the circle once you've completed that path. So this is our letters see here and really see is just equal to two pi times the radius. So if you know one of those variables, you can always figure out the other one, all right, so let's talk about the other two, and they're very closely related to each other, and they have to do with time. The first one we talk about is called period, and the symbol we use is this capital T. Basically, the period is just how long it takes for you to complete one cycle or one lap around that circle. And so one way you can think about this is that it's the number of seconds divided by Earth per the number of cycles. And so the unit that will use for this because it's seconds per cycle is just the second. And so one really quick way to figure out the period is just if you take the number of seconds elapsed and you divided by the number of cycles. So quick example here. If it took us two seconds to complete one lap, then our period is just to over one, and that's just two seconds. All right, so the other related variable is called the frequency, and the frequency is basically just the opposite of the period. Instead of it being seconds per cycle. It's the number of cycles that you complete per second. So notice how these are basically just opposites of each other. So the unit that we use for this is not going to be a second. It's actually going to be a hurts. And our hurts is essentially just an inverse second. It's one divided by seconds. And so because we're basically just flipping these two things we can do is we can take this equation here, seconds per cycle, and we just flip it upside down. So the way to calculate the frequency is just by doing the number of cycles divided by the number of seconds. So if you take a look at these two variables here, notice how they're basically just opposites of each other, you just flip the fractions. And so in general, you can always figure out the period from the frequency and then vice versa. And here the equations to do that if you want the period, you're just going to take the inverse of the frequency. And if you want the frequency, you're just going to take the inverse of the period. We're basically just gonna flip the fractions. Let me show you how this works, and we'll do a couple of examples here. We're going to calculate the period and frequency of our motion. If we complete four rotations in two seconds, let me show you what this means. Imagine you were walking in a circle and you did. 1234 rotations. Right, So this is basically four cycles, and it took us two seconds to complete these four cycles. So how do we calculate the period? Remember, the period is really just going to be the number of seconds divided by the number of cycles or rotations or whatever word you're using. And so we're just gonna use two seconds divided by four cycles and you'll get one half. So if it takes you two seconds to complete four cycles, then basically each one of these is one half of a second and so on and so forth. All right, so that's the period. The frequency is going to be the opposite. The flipped fraction of that. We're gonna do the number of cycles divided by the number of seconds. So we're just really going to do four cycles divided by two seconds, and then you'll get to hurts. So one way you could also have done this is you could just take these fractions, right? You could have taken this one half of a second and flip the fraction that becomes too over one. And that's really just to hurts. All right, so let's take a look at the next one. Now we're doing 10.5 rotations in three seconds. So what this means is that we got half a rotation, right, but the other half is kind of missing, so we have 0.5 cycles and then we have three seconds to complete, so we'll do the same exact idea here, right? The period is really just going to be the number of seconds divided by a number of cycles. So it's three seconds divided by 0.5 cycles, and then you get six seconds. Basically, if it takes you three seconds to complete half of a circle and it's going to take you another three seconds to complete the other half, then your total period is gonna be six seconds, all right? And so the frequency is just going to be 0.5 cycles divided by three seconds. Basically, you just flip the fraction and then you'll get as you expected. 1/6 of a hurts. All right, So those again, how these two fractions are basically just flip the versions of each other. All right, so that's it for this one. Guys, let me know if you have any questions.