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All right, hello.
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Today we're going to discuss the rotational equivalence of all of these translational things.
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And to start, we're going to start with acceleration.
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So if we have translational acceleration, that's the change in speed over change in time.
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Well, that still applies for rotation, but instead of the change in speed, it's going to be the change in angular speed over the change in time.
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So that's usually what we denote as alpha.
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For our force, what is our analogy to force? well, if we have something, some lever here, and we're going to apply a force, instead of applying just a force, we have to apply it at some distance.
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And that is going to cause some rotational acceleration.
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And what we're applying there is called a torque.
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So this is called torque.
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And torque is equal to, just like in newton's second law, it's the force times our lever arm, the distance away that we apply.
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And because of newton's second law, we know the sum of the forces equals mass times acceleration.
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This is our sum of the torques is equal to our equivalent mass, which in this case is moment of inertia, times our acceleration, which in this case is alpha.
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Now, our moment of inertia is our equivalent to rotation.
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And the reason that it's not just mass in rotation land is because it depends on how the mass is distributed.
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If you think about trying to push a door open, if you were to have a very, very heavy door, it would be harder to push than a light door.
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So there is moment of inertia does depend on the mass somehow, but it also depends on where that mass is distributed and the length of that.
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So if you had a door and all of the mass was on one end, think about someone was hanging on to the outside of the door and you tried to push it, it would be harder than if they were hanging right by the pivot.
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And so our moment of inertia is some constant value k, and that depends on the configuration of the mass, times the mass, times the radius squared.
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That radius is usually the distance from the pivot point, wherever it's rotating about.
02:05
Work, what is the rotational equivalent to work? well, in a translation land, work is equal to force times the distance traveled, right? in a rotational land, it's still denoted as work, but we use our equivalent force, which is torque times the distance traveled, which in this case, we're traveling some change in angle...