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So this M three right here closer to the axis, axisīeing right at this point in the center, closer to theĪxis so it's speed is smaller than points that areįarther away from this axis, so you can see this is kinda complicated. You can't see that very well, I'll use a darker green This point right here, we'll call it M three, movingĭown with a speed V three, that is not as big as V two or V one. So I'll call that V two and points closer to theĪxis are gonna be moving with smaller speed so It's gonna be moving down cause it's a rotating circle, The leather right there, I'm gonna call that M two, M one, that little piece of mass right now and I'llĬall the speed of it V one.
![total kinetic energy of particles total kinetic energy of particles](https://i.ytimg.com/vi/r8w3G_8HR9A/maxresdefault.jpg)
Piece of leather right here, it's gonna have some speed forward. This, so this point at the top here imagine the little Is moving with some speed, so what I mean by that is Still just the same old regular kinetic energy for Is that this rotational kinetic energy isn't really a new kind of kinetic energy, it's This is the rotational kinetic energy of an We didn't really prove this, we just showed To ride this cause that is not really a derivation, If I replace speed with rotational speed, I get the angular speed and
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So if I replaced mass with rotational mass, I get Substituting the rotational analog for each of the variables, Rotational analog of some linear formula by just Not really a derivation, you're just kind of guessingĮducatedly but you could often get a formula for the Squared, maybe since I have something rotating I'd Instead of mass there's moment of inertia so maybe I replace that. So I might guess alright instead of mass, I'd have moment of inertiaĬause in Newton's second law for rotation I know that Let me just call that k rotational and what is that gonna be? Well I know for objects that are rotating, the rotational equivalent of The formula for regular kinetic energy is just one half m v squared. This for the first time, my first guest I'd say okay, I'd say I know what regular How do we determine what the rotational kinetic energy is of an object? Well if I was coming at Mean that that ball has extra kinetic energy? Well it does, and howĭo we figure that out, that's the goal for this video. Pitches head toward home plate with the baseball spinning The fact that most pitches, unless you're throwing a knuckle ball, does the fact that most We know that cause if you get in the way, it could do work on League baseball player throws a fast ball, that ball'sĭefinitely got kinetic energy.