![]() ![]() That's what this termĭown here's gonna be. How resistive it is to being accelerated. And remember, this mass was proportional to the inertia of an object. This M R squared, what is that? Well it's serving the same role that mass did for regular acceleration and the regular Newton's second law. Newton's second law for rotation is this torque divided by this term here. The angular acceleration of this mass is gonna equal the torqueĮxerted on that mass divided by this weird term, this M the mass, times R squared. This or I could put it in this form over hereĪnd just solve for alpha, and get the alpha. If I wanted a form of Newton's second law I could leave it like Rs and just write this as M times R squared timesĪlpha, the angular acceleration. We've got torque is gonna be equal to R times M, times R times alpha. So this whole term right here was just tangential acceleration, and now look what we've got. Side as R times alpha 'cause R alpha is the The tangential acceleration as R times alpha, and These are both tangential here, and these forces are all tangential. So since we took the tangential force, that's gonna be proportional Is this tangential acceleration? It is 'cause this was So this is the relationship between alpha and the tangential acceleration. Is always gonna equal the distance from the axis to that object that's got the tangential acceleration, multiplied by the angularĪcceleration alpha. Regular acceleration with in order to get angular acceleration? Maybe you remember when we talked about angular motion variables. Remember over here we want a formula that relates torque toĪngular acceleration, not a formula that relates So I've got torque equals R times M, times the acceleration,īut that's no good. And this was good, lookĪt now we have R times F. Now that's gonna equal R times the right-hand side. Multiply the left side by R I'll get R times F, and If you're creative you might be like, well let's just multiplyīoth sides by R down here. What do we do with this? Well look at down here, we'veĪlready got an F down here. So this is simple, the torqueĮxerted by this force F is gonna be F times R. Of the angle between F and R, but the angle between FĪnd R is 90 degrees here, and the sine of 90 degrees is just one, so we can get rid of that. But we applied it at the very edge so this would F times the entire radius. If this force wasĪpplied inward somewhere, it would be only thatĭistance from the axis to the point where the force is. Now in this case, that's the entire radius 'cause we applied this forceĪll the way at the edge. How do you find the torque from a force? Remember that the torque from a force is gonna be equal to theįorce exerting that torque times R, the distance from the axis to the point where the force is applied. What's new here? Well remember, we want to relate torque to the angular acceleration, so let's write down the torque formula. Well we know that the net force has to be equal to the mass of the object times the acceleration of the object. One force on this object, and it's this force here. And let's make it simple too in this way, let's say this force is the net force. Let's say the angle'sĩ0 so that sine theta will end up being one Times F times sine theta, but let's make it simple. So let's say this is theįorce causing the torque, we know how to find it now. So in order to go angularlyĪccelerate something you need a force that's tangential because this force is So how do we do this? In order to have an angular acceleration we're gonna need a force that's Just like we determine regular acceleration by knowing the force and Newton's second law. Torque we could determine the angular acceleration So let's do this, let'sĭerive this formula so that if we know the So it would be speeding up in its rotation or it'd be slowing down in its rotation. I want to derive this rotational analog of Newton's second law for an object that's rotating in aĬircle like this cue ball. So that's what I want to do in this video. The angular acceleration is just like up here by knowing force, we could tell what the Then by knowing the torque we could figure out what This rotational analog of Newton's second law, Torque on top 'cause torque is gonna cause something And you could probably guess that this angularĪcceleration's gonna have probably something with Of angular acceleration for a certain amount of torque. Something that would tell us alright, we'll get a certain amount What we would like to have is some sort of rotational analog of this formula. We know from Newton's second law that the acceleration is So we know how to find the torque now, but who cares? What good is torque? What good is it gonna do for us? Well here's what it can do.
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