Hey, everyone. So let's check out this torque problem here. So we're applying some force to the end of a wrench. Right? So we're taking this wrench that's at this angle here and we're pulling it with a force of 100 newtons. The wrench is 25 centimeters long, so the length of this whole thing here is 0.25 meters, and I want to calculate the amount of torque that my force is going to produce. In other words, I've got the torque (tau) as my target variable, and the other thing I know here is that the angle that's shown is 53 degrees. Alright. So how do we do this? We know the torque is equal to F times R times the sine of theta. Alright. So we actually know what the force is, that's already given to us. That's pretty simple: 100. And then we've got this R and the sin(theta). That's what we need to figure out here. So what is our R and then what is our sin or what is the angle that we plug into our sin equation? Alright?

Let's tackle the R first. Remember that R is always the vector from the axis of rotation to where our force is applied. In this problem, the axis of rotation is an axis perpendicular and through the bolts. So here's my bolt right that's here at the end of the wrench. So now I just need to draw that vector out to where your force is applied. So it's basically this vector over here. Alright. So that's my R. What's the length of that R? It's basically just the length of the entire wrench, which we know is 25 centimeters. Alright. So these two things are the same. R is equal to L. So that's what we plug into our R.

So now what do we plug into our theta? And this is where you really need to slow down and be very very careful. A lot of times, these problems will try to trick you with the angles, so you need to be very paranoid. You need to be wondering, is this problem trying to trick me? Because the chances are it probably is. Alright. So let's check this out, and we'll go really slowly here. What is the angle? Remember that the angle is always between the F vector and the R vector. I'm gonna write it out here. So this is between F and R. Okay? So in this problem here, it's not super obvious what 53 degrees really applies or really pertains to. So what I just like to do is sort of draw like a secondary sketch at the bottom. So we've got our R vector that kind of looks like this. Right? This is my R. You've got the F vector that goes out horizontally like this and we know that this angle here is 53 degrees. Now this problem or this schematic or this little diagram here doesn't show us really what 53 degrees sort of pertains to. Alright?

So what I always like to do is I always like to line up the vectors so that they start from the same place so that their tails are in the same place. There are two ways to do this. One, you can actually just keep this R vector going down sort of like this, right, so that they sort of are going from the same place, but actually there's an easier way to do this, which is we can actually just scoot this force vector up over here. So we're just gonna sort of transplant it over here. Remember, from rules of vectors, you can totally do this. You're not changing this vector. All you're doing is you're just moving it sort of upwards like that. Alright? So that's what I'm gonna do here. Actually, I'm gonna keep that there, I'm just gonna sort of scoot that up like that. And now I can see here from this sort of diagram that this 53 degrees is not the angle between F and R. 53 degrees is the angle between R and the vertical. Okay? So this is actually not the right angle we're going to use. That's the entire point of this problem. Alright? These problems are trying to test whether you really know what you're doing or whether you're sort of randomly plugging in the numbers that you see in a problem. Alright? So just go slow, be a little paranoid. Alright? Double check that you really understand the angles and the variables involved.

The angle that we really need is this one over here and this angle here is going to be 37 degrees. It's the complementary, right, just because this makes a 90 degree angle. Alright. So that's what we plug into our torque equation. So that goes, that's 37 degrees. And now we can just go ahead and plug everything in. So, when you multiply all this out, what you're going to get is you're going to get 15 Newton meters, and that is your torque. Alright? So, hopefully, that makes sense. Let me know if you have any questions.