8. Centripetal Forces & Gravitation
Uniform Circular Motion
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We got a fun little problem here involving the moon's orbits. So we're told that the moon travels in a roughly circular orbits and we're told the radius of that orbit. Right? So this is the earth right here. This is like little earth like this. You know? And so we have the moon that's gonna be traveling in a nearly circular orbit which means it has some tangential velocity like this. And then has also some centripetal acceleration. Now we're told what the orbital distance is basically between the Earth and the moon. That's this that's this big r here. And because of this really large distance, we also have a really small centripetal acceleration. So we were trying to figure out how fast the moon would be traveling if it suddenly broke free of the orbit and then stopped orbiting. So basically, what this means here is that over 3 variables, we're actually trying to figure out the tangential velocity. Remember that the tangential velocity is the velocity that you're gonna have if you were to suddenly stop turning in circular motion. Right? Basically, it's just always changing direction like this. So if you were to suddenly stop turning in your orbit, you'd go flying off in this direction. So we're trying to figure out how fast what's the magnitude of that tangential velocity. Alright? So, basically, we're just gonna go ahead and look at our equation. We know that ac equals v, v tangential divided by r. Which variable are we trying to look for? We're looking for the v tangential, so we're just gonna get everything over to the other side. Right? So we have that v tangential squared equals a c times r. And so now we just take the square roots. This is gonna be the square roots of our centripetal acceleration, which is 0.0026, and then our radius, which is 3.85 times 10 to the 8th meters. If you go ahead and work this out, you're gonna get about exactly 1,000 meters per second. And if you go ahead and look up or Google what is the orbital speed of the moon, this is basically what you're gonna find. It's about a 1000 meters per second as it travels around the Earth. Alright? So that's it for this one, guys.
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