An object moves a total distance of 1,000 m around a circle of radius 30 m. How many degrees does the object go through? BONUS:How many complete revolutions does it make?

Hey, guys. So I hope you tried this one. Here we have an object moving a total distance of 10, 1,000 meters. Because it's in meters, this distance will be represented using delta x. So it's 1,000 meters. It's a linear distance around a circle. So here's the object, around a circle of distance, of radius 30. So if you go around a circle of radius 30, your distance from the center, your radial distance to the center is the same as the radius of the circle, which is going to be 30 meters. And we want to know how many degrees do you go through. How many degrees do you go through is asking for delta theta but in degrees. K. So if I have delta x and r and I want delta theta, there's an equation that connects these, Delta x equals r delta theta. Therefore, delta theta is delta x over r. Delta x is 1,000 meters and r is 30 meters. And if you divide the 2, the answer is 33.3. Now I want to talk about something real quick just so that you don't get confused potentially, is that if you notice, meters cancels with meters. So you would think that maybe I end up with 33.3 has no units. It's unitless. And actually, it isn't. The unit is radians. Right? Because if you remember, I told you that this equation, if you're ever solving in this equation here for delta theta, it's gonna spit out an answer in radians. And radians is actually, by definition, a ratio, a fraction of 2 units in meters. So 1 radian is actually, defined as a meter over a meter over a meter. K. It's a ratio of 2 distances. It's a ratio of a linear distance around a circle to the radius of the circle. Okay? So don't don't be weirded out by the fact that meters and meters cancel. As long as this is a delta theta, it should be radians coming out of that equation. Cool? So a little tricky, but that's to get there. And then I want to know how many complete revolutions. Actually, there's one more thing. We want this in degrees, to find new answers in degrees. So let's convert that and then we're done. 33.3 radians convert to degrees. I have to use the fact that pi equals 180. Pi radians goes at the bottom so that the radians cancel, and 180 degrees goes up top. Okay. These 2 cancel and you're left with degrees. If you multiply all this, the answer is 1908 degrees and that is the final answer. I hope you guys try this. I hope you got it. I hope you also try the bonus part. So how many complete revolutions does this thing make? And to know how many complete revolutions you have to divide. Okay. One way to remember is, if you do 306, 36100 degrees, you just divide it by 360, and you see that you get 10 revolutions. Right? So you just divide it by 360. So 1908 divided by 360 tells you how many times you spun. The answer is 5.3. So what's the answer? Do you leave it as 5.3? Is it 5? Is it 6? Well, because I want complete revolutions, right, I have 5 complete revolutions and 3 is like a partial piece of a revolution. That's 30% of a revolution. So the answer here is that there are 5 complete revolution revolutions, 5 complete revolutions. So if I want to know complete revolutions, what you do is you just round down. Okay? That's all it is. Alright. Let me know if you have any questions on this one.

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An object moves a total distance of 1,000 m around a circle of radius 30 m. How many degrees does the object go through? BONUS:How many complete revolutions does it make?

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An object moves a total distance of 1,000 m around a circle of radius 30 m. How many degrees does the object go through?
BONUS:How many complete revolutions does it make?