Hello class, Professor Anderson here. Let's take a look at a torque problem. And let's say you're trying to remove a bolt. Okay so here's our bolt and you put a wrench around it and now you're gonna pull on that wrench. And let's say the geometry of where the bolt is located prevents you from pulling on the wrench at a right angle, instead you have to pull off at some angle like so, okay. And that angle is phi so the bolt comes loose if the torque on the bolt is equal to some number and let's use 33 Newton meters for the bolt to break free. And let's say that that angle is bigger than 90 degrees, let's say it's about 105 degrees. And let's say that your wrench length is R and that is 29 centimeters which is zero point two nine meters. And now the question is how hard do you have to pull on that wrench to actually loosen the bolt. Okay so we're looking for F. All right. Torque is equal to a few things right. Torque is equal to the force times the lever arm or it's equal to the R times the perpendicular component of the force. Either of those are the same thing as saying torque is equal to R F sine of phi. And now we have all that information so we can solve this for F. F is just torque divided by our sign phi. And we have those numbers. Torque was 33. R was 0.29. Phi was 105 degrees. And if you plug in all those numbers and run them through your calculator you should get 117.8 Newtons That's how hard you have to pull on that wrench. All right hopefully that's clear, if not come see me in my office. Cheers