Lessons · Engineering · moments and the lever
A moment: how hard a force is trying to turn something
Moment is force times the perpendicular distance from the pivot to the line of the force: M = F × d, in N·m.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A technician cannot free a seized bolt with a short spanner and frees it easily with a long one. The force is the same; the moment is not. Every beam, hinge and crane arm is that spanner.
How to think about it
Find the pivot. Find the line the force acts along. The distance that matters is the perpendicular one from the pivot to that line, not the length of the bar; if the force is not square to the bar, use only the part of it that is.
Worked example
M = F × dd is the perpendicular distance from the pivot to the line of the force.
A 0.3 m spanner, 50 N at the end, square to the handle: M = 50 × 0.3 = 15 N·mFull length, full force, because the push is at right angles to the bar.
Same 50 N on a 0.15 m spanner: M = 7.5 N·mHalf the arm, half the turning. That is the whole story of the long spanner.
A lever: 400 N load 0.2 m from the fulcrum, effort 1.6 m out: F = 400 × 0.2 / 1.6 = 50 NBalance means the moments match. Eight times the arm, an eighth of the force.
Your turn
A 0.5 m bar, 120 N at the end, square on. Write the moment.
M = 120 × = 60 N·m
Solve one, graded on the server
The trap
Using the length of the bar when the force is not square to it. Only the perpendicular part counts; a force aimed straight at the pivot turns nothing at all, however large it is.