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Video transcript

welcome to the presentation on torque so if you watch the presentation on the center of mass which you should have you might have gotten a little bit of a a glancing view of what torque is and now we'll do a little more detail so in general from the center of our mass center of mass video we learned it if this was a ruler and this is the ruler center of mass and if I were to apply a force at the center of mass I would just shift the whole ruler in the oh I would accelerate the whole ruler in the direction of the force so if if I had the force applying at the center of mass there the whole ruler would accelerate in that direction and we'd figure it out by making the the force that we're applying to and dividing by the mass of the ruler and in that center of mass video I imply well what happens if the force is applied here away from the center of mass well in this situation the object assuming it's a free-floating object it's on the space shuttle or something it will rotate around the center of mass and that's also true if if we didn't if we didn't use the center of mass but instead we fixed the point so let's say we had let's say here's another ruler although it has less a height in the previous one instead of worrying about its center of mass let's say that it's just fixed at a point here whoops let's say it's fixed here so it's like I don't know this could be this could be like the hand of a clock and it's nailed down to the back of the clock right there so if we were to try to rotate it it would always rotate around this point and the same thing would happen if I were to apply a force at this point maybe you know I could break the nail on the back of the clock or something but I won't rotate this this needle or this ruler or whatever you want to call it but if I were to apply a force here I would rotate the ruler around the pivot point and this force that's applied a distance away from the pivot point or we could say from the axis of rotation or the center of mass that's called torque and torque the letter for torque or is this Greek I think that's tau it's a curvy T and torque is defined as force times distance and what force and what distance is it it's the force that's perpendicular to the object I guess you could say to the distance vector right if this is the distance vector let me do it in a different color if this is the distance vector the force is going to be the component of the force it's perpendicular to this distance vector and this is torque and so what are its units will forces Newtons and distance is meters so this is Newton meters and you're saying hey Sal Newton's times meters force times distance that looks an awful lot like work and it's very important to realize that this isn't work and that's why we won't call this joules because in work what are we doing we are translating an object if this is an object and I'm applying a force I'm taking the force over a distance that's in the same direction as the force right here the distance in the force are are parallel to each other you could say the distance vector and the force vector are in the same direction in this situation of course that's translational the whole object is just moving it's not rotating or anything in the situation of torque let me switch colors the distance vector this is the distance from the fulcrum or the pivot point of the center of mass to where I'm applying the force this distance vector is perpendicular to the force that's being applied so torque and work are fundamentally two different things even though their units are the same and this is a little bit of notational this distance is often called the moment arm distance and I don't know where that came from maybe one of y'all can write me a message saying where it did come from and often saw in some of your physics class the locks off didn't call torque as as a moment but we'll we'll deal with the term torque and that's more fun because eventually we can understand concepts like torque horsepower in cars so let's do a little bit of math hopefully I give it given you a little bit of intuition so let's say I had this ruler and let's say that this is its pivot point right here right so it would rotate around that point it's nailed to the wall or something and let's say that I apply a force let's say the moment arm distance so let's say that this distance let me do it in a different color let's say that this distance right here is 10 meters and I were to apply a force of 5 Newtons perpendicular to the distance vector or to the dimension of the moment arm you could view it either way so torque is pretty easy in this situation torque is going to be equal to the force 5 Newtons times the distance 10 so it'll be 50 Newton meters and you're probably saying well Sal how do I know if if this torque is going to be positive or negative and this is where there's just a general arbitrary convention in physics and it's good to know if you are rotating clockwise torque is negative well let me go the other way if you're rotating counterclockwise like we are in this example right we're getting counterclockwise the opposite direction of which a clock would move in torque is positive and if you rotate clockwise the other way torque is negative so clockwise is negative and I'm going to go into the whole physics the the whole cross-product and the linear algebra of torque right now because I think that's a little bit beyond the scope but we'll do that once we do more mathematically intensive physics but so good enough up you know there's a torque of 50 Newton meters and that's all of the torque that's acting on this object so it's going to rotate in this direction and we don't have the tools yet to figure out I guess you know how quickly will it rotate but we know it will rotate and that's vaguely useful but what if I said that the object is not rotating and that I have another force acting acting here and let's say that that force is let's say that that force is let's say that force is I don't know let me make up something that's 5 meters to the left of the pivot point let me do a different color this is five meters to the left of the pivot point and if I were to tell you that the net that this object does not rotate so if I tell you that the object is not rotating that means if the net torque the net torque on this ruler it must be zero because it's not well it's it's rate of change of rotation is not changing I should be a little exact if I'm applying some force here and still not rotating then we know that the net force the net torque on this object is zero so what is the force being applied here well what is the net torque well it's this torque which we already figured out and it's going in the clockwise direction so it's five we do it in a brighter color five times ten and then the net torque the total the sum of all the torques have to be equal zero so what's this torque so let's call this F this is the force so plus well is this this force is acting in what direction clockwise or counter counter clockwise what's acting in the clockwise direction right this Force wants to make the ruler rotate this way so this is actually going to be a negative torque so let's say put a negative number here times F times its moment arm distance so times five and all of this is has to equal zero the net torque is zero because the object the object is its rate of change of rotation isn't changing or if it started off not rotating it's still not rotating so here we get fifty minus five F is equal to zero 50 is equal to five F F is equal to ten and if we follow the knew the units all the way through we would get that F is equal to ten Newtons so that's interesting I applied double the force at half the distance and offset it half the force at twice the distance and this should this should all connect or start to connect with what we talked about with mechanical advantage right you could view it the other way if let's say these are people applying these forces this say this guy over here he's applying ten Newtons he is much stronger he's twice as strong as this guy over here but because this guy is twice as far away from the pivot point he balances the other guy so you can kind of view it as this guy having some mechanical advantage or having a mechanical advantage of two and and watch the mechanical advantage videos if that confuses you a little bit but this is where torque is useful because if an object's rate of rotation is not changing you know that the net torque on that object is zero and then you can solve for you know the forces or the distances I'm about to run out of time so I will see you in the next video
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