The second one with the pin is especially hard, imo.

I don't even know what the basic equation here is. The book dosen't tell you this. It's always [itex]\Sigma[/itex][itex]\tau[/itex]=....... something else. So I do have to create my own equation each time, basically. Is this correct? Depending on whatever the problem is. I don't get it. Can someone please explain this to me?

For these types of questions, essentially you make the torque provided by the cable equal to the torque caused by the weight of the beam. This must be true, because otherwise the beam would be rotating on its pivot. I can't really help you with anything until you show me an attempt at a solution.

I essentially just told you in my last post. Think of torque as acting either clockwise or counterclockwise about the pivot. Take the perpendicular components and make them equal each other. Solve for missing variable. If you're looking for a basic equation, there isn't really one. All torque questions are based off the fact that the sum of torques must be equal to zero.

What are the perpendicular components for the 1st example? Torque(0)=Tsin51*length of beam -weight of person*meters from the pivot - weight of beam*(I don't know). Don't know what the last component in this equation would be. But then I would solve it for T. I have no idea if this equation would get me the tension of the cable., but that's what I can come up with.

For the second question, the cable is acting at an angle right? This means that the cable has a horizontal force. Since the beam is not moving, therefore the pin must be supplying a horizontal force that either pushes out against the beam or pulls it toward the wall to stop it from moving sideways.