Question

When taking moments around B, with AB as a road and AC a string, why don't we consider Tcos(alpha) when balancing anti clockwise and clockwise forces? (the diagram is in equilibrium)

Answer 1

That component of the tension has a radial direction and therefore exerts no torque.

Answer 2

You can ignore forces that pass through the axis you are taking the torque about.

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Think about a door. If you had the door open and pushed onto the door directly towards the hinges it wouldn't open/close any further. Torque will not be affected by the forces that go towards/away from the axis.

Answer 3

I know this isn't techincally geometry but there was no mechanics flair sorry Reddit mods