Hi, everyone. So we're trying to stop exercised him. Point one here and this exercise asks us to calculate to talk, including the magnitude and the direction about a pivot point. Oh, so this is this fat black points that I drawing out here, and in each case, we have a force that has a magnitude of ten. You ten. So that is indicated by this red arrow. And we have a raucous four meter. So that's justice Black lives. So we can see that it's same. Roth and force improve it. But it's the forces acting on different ways, different directions and different point of contact. So how do we find the torque? I think Let's first right, tongues off formula for talk. So we have the idea of how to get started. Yeah, we have, um So the book gives a variety of formulations for the talk one as it comes out in which, after the magnitude and l is a lever arm. But we'LL find that the more it's a more useful formula is f conjectural. I'm unable to stop subscript. There's just use ft. To indicate African gensia times are where R is the distance between the point of contact is a pivot point, and we have this this way because usually are is much easier to find. There's a lever arm and FT. We can find it just by decomposing Za force into the tangential part ends the radio part. But let's first get started and see how it works out. Um, Phil, for case for the very first case that is this one. We have a force that is ninety degree. It's acting completely tangentially that Mieze. So in this case, the force itself in Tao ten. You tin is tangential, forced, so we do not need to bother. Took decompose a force because we already know everything's gonna be condition. So that's great that we can just planned everything to the forms are just gave us. Larry wants space over here, so that's creating that. We do not need to decompose the force, and we can just right toe because FT is just after So is ten mutant times R R is this distance from the pivot point is a point of contact. This red arrows point is, that's the gentleness of drawing, which is four meter, and that gives us forty nutrition from here. Don't forget the unit. Um, so this will be the torque, the magnitude of the talk before the first case. And let's check out the second case. Good. Here's inside a bit different in that we have this angle that is not ninety degree anymore. This is the questions is one hundred twenty degree. Some things we do have two decomposes for snuck us. It's not completely tangential and using the HVAC traditions that we should be very familiar with. By this point we have we can decompose it into two components. One is tangential to this rot or perpendicular to use this rod, and one is a radio component, which is along the rod. And because he's this component, since one is sittin gentle, companion is us. This is the force, the part of the force that causes road. Who wrote it because after our talk is what causes something to wrote it, and this is a component we're looking for. And what about this? What was this one that's along? The rocket doesn't really do anything. It is used to compress a rock, but it does not cause it to rotate. So that's the reason we do not eat. Okay, so let's first try to calculate It's a tangential party. Traditional part here we have. This is equal to, uh, needs a little bit. Geometry overhears this isthe one twenty. Uh, that means this is sixty. So if this is sixty, we have So we have f tangentially equals f. Is that how after Newton tons sign off sixty degree What a son of sister degree of we put into the calculator? We know it's square held three over two or it's a run zero point eight six. So plugging that we know that often Joshua is around eight point six him from that we can calculate the torque park equals after gentian. And again, what's what is R R is the distance from the points of spread arose put. He had to use a pivot foot, which is again four meter. So lives are because eight point six you clone Huns times for leader. So that gives us a total of round thirty four point six. I'm sorry on So that is your temper meter again. Units, this is Magnus. Ship talk for the second place and so certain cases actually was a similar Is that we can use the same kind of procedure to solve it. In this case, we have thirty degree over here and would use the same decomposition you can see exist. Now we have a radio components that is used to extend the rod, but tangential component. It's again science thirty degree. So now we have fifteen. Because when Science thirty three, so thirty degree again have you put into the calculator or if you remember it, it's just with zero point five. So this is five Newton, and then we have clothes. Tee times are because Putin, good times, formula. Just Clinton. Okay, so this is what is happening for the first Street cases. Let's move on to the next three. Florida is the first one, which is well in the lower left corner, which says things not get liver different. So you have a different point of contact. So this point of contact is it's two meters to its end of the rod, since we know that's the whole rod is for meter. You know this part is two meter as well. So this part, this is our we're looking for from the point of contact to the rock was a pivot off the rod. Sinus two meter. So says which is the same force decomposition, Except that now we have our equals two meters to perform eater. Um but if we find the same procedure now we have sis is sixty and again decompose So force in the half The tangential component is it tons sign sixty three. So we've already calculated this we know is a sixth teacher. And what changes is now we are doing it. Wait when we do the second problem catalysed talk where I'm not applying it by two meters instead of formers because And that gives us seventeen point two. Okay, what about this case? Um, we can started the commercial force, but less first is back this case a little bit. We are. We have a point of contact right here. So it is. We're acting forces acting right. Pivot. So what is a lever order? See, just just between some point of country and activity Zero, because we're acting right on it. So no matter what is the force effective force? We can see when we do talk equals when we do talk equals f l. Um uh, our or fifty times are you will see that are zero. So no matter what so forces we were in the Wizard Hawk zero So we'll really need your calculated out. You could just tell that zero And that's the same for the last case in this case, we are acting on this point, but soft Entire fourth is radio to the frog. So is that because we have afternoon Gensia because zero because there's not inject your component of this force is that against gives us tall equals zero And now a dong was Cutler is mme attitude offs. The torque we have, um, now is there a magnitude for four off these cases? But we have zero talk for the next two concert last because it's so in the last two kisses, one matter how hard we push is not. The drawing is not goingto wrote it. And if you just try to visualize pushing a rod a fix to pivot for pushing around a lot of direction of it, it's to get some intuition of it. Try to imagine doing that, and hopefully your risk of clues that is shouldn't be moving, so but we're not done yet. Cesar. We also need to find a direction off the talk so hard to find the direction of the talk. We have existing clots and white and rule, which is introduced by the book. So what it's saying is that for every talk say we have, they're not over here and imagine would have a force inlay Say you have a force nexus. What you should be doing is you should try to align. You're right. You should try to reach her right hand and points of fingers of the right him eggs interaction off are so we have our exist direction. So try to reach, have your right hand and point your forefingers, not just some. The four fingers his destruction not try to Kurzem is direction off death. So this is more like this is a various three d joint. But it's if, um, they look down and you try to put your this is a sound. Imagine it's popping out of the paper. Um, you should have your right hand curved his destruction and it's your palm. This's arm Season four fingers. This's just like top few of your right hand. You should be a lining your right hand so that your forefinger so that your arm is alive in distraction but you're free for fingers are pointed, is a upward direction of the screen, and then you should have some facing yourself. Right now that will be Chu for any force that's acting up. If you just try to cur finger that about your season. For any forces acting up, you will have. Osama is pointed towards you, and that is how you should be calculating the torque. The direction of the talk is you allow your fingers alongs are in the you crow it in direction off the is. Then your son will be pointing in the direction of the talk. So you see, for any force acting up, you have a some pointing to issue so as a talk will be pointing out of the page out of the screen is that will be applied in for both three cases in the first world. If you try to trade out with your hand and you see that's the talk will be pointed out as a pitch or sometimes we try. We can not this as having a circle in the dot that's that indicates going out of the page. And what about this case? These are just they're Oh, so this is the last year. Just cereal. So we don't care about but this one is. When you have your arm again, it's still right hand. You have a right hand and yeah, this is Brother. This is a right hand and you try to align the four fingers alone The direction of this fraud. So again, this the pivot is other left. So it has to be so four Finger has to be reaching right. It is in you try to curse him in the direction of the forces this times his forces going down. So try to curl your fingers. So you have Is this is that your some should be facing in queues a scream. It should be facing same. It's the same directions. Are you? It's a screen. So this is into the page and sometimes we do you know, that is have a silk robe, isn't it across? You know something's going away from you can think of it as an error or that's going away from you and your your seniors tails. So that is the direction for talk for this case. The torque points. Well, that's just that is the all six cases of trained yourself. We have the magnitude and we have the directional have the two direction is that we have several end sad. Is it you?