Pin holding a horizontal bar

by Patrick Ford
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Hey, guys. So here in this example, we're trying to balance a sort of a shelf on a wall by using a pin. So let's check it out. So that the red pin here Andi were using it to try to balance the bar that has a mass of 20. So am equals 20 in a length of 3 m and it's held horizontally against the wall by the pen right here. Okay. The idea is that there's going to be an mg right in the middle that's pulling the bar down. Um, this is the axis of rotation somewhere over here. Axis. Okay. And this MGI is producing a torque that would cause this to spin. But the pen, which could be like a nail or something, is holding it up, and the way it holds it up is by providing a counter torque. Okay, so here, if we're holding it up, we're going to say that the sum of all torques equals zero because the bar is not going to accelerate. Um, it's not gonna rotates. Not gonna have angular acceleration. The torque of M. G is this way, which is negative. So you'd want the torque of the pin to be positive so that they cancel. Okay, so we're gonna write torque of M G Negative plus torque of pin positive equals zero. This gives us that I'm going to send the negative to the other side. Torque of pin equals torque of N G. There should make sense. All we're doing is getting these two guys to cancel each other out. And what we're looking for here is what is the torque on the pin that's needed and the way we're going to calculate the torque on the pin is just by calculating the torque of M G. Okay, so torque of pin will be m g gonna expand the right side. Our sign of theta Now the masses 20 gravity 9.8 r is the distance from the axis of rotation to the point where the force happens. We have a uniformed mass distribution, which means mg happens in the middle of the bar. The bars 3 m long. So the our vector is 1.5. Put a 1.5 here and the angle that these two guys make is degrees. So sign of 90 is one. Okay. And if we multiply this whole thing. We get 294 Newton Meter, and that's it. That's the answer here. Okay, So very straightforward question for us to see to calculate one torque based on some other information, Right? So that the finish one. Let me Do you have any questions? Let's keep going.