Lesson 2 · 16 min
Torque and equilibrium
Forces want to translate. Torques want to rotate. Statics is both sums sitting at zero.
The moment of a force
Torque τ = r F sinθ, the moment arm times the force. Direction is the axis the force is trying to rotate the body about — out of the page, or into it, in planar problems. A bolt head is a reminder: force far from the axis, perpendicular, is what turns it. Force through the axis turns nothing.
You may take moments about any point. The clever point cancels unknown reactions.
Worked example
Cantilever sign
- Given: Uniform 2.4 m beam, 18 kg
- Given: Sign 12 kg at the free end
- Given: Pivot plus a cable at 30° at the free end
Find: Cable tension (sketch: hinge at wall)
- Moments about the hinge kill the hinge reactions.
- Clockwise: (18g)(1.2) + (12g)(2.4)
- Counter: T sin30° × 2.4
- T = [18g(1.2) + 12g(2.4)] / (2.4 × 0.5)
T ≈ 353 N (the hinge then carries the rest of the weight and the horizontal from the cable)
Check
A 3 m uniform plank of weight W rests on supports at both ends. A person of weight W stands 1 m from the left. The left support reads
Bench
Fulcrum
Στ = 0
- τ left
- -11.8 N·m
- τ right
- 20.6 N·m
- Στ
- 8.8 N·m
- State
- Rotate