Moment of a Force

M = F d = F r sin ϕ = r \times F

The moment about a point is force times the perpendicular lever arm d. Equivalently |r||F|sinφ or the vector cross product. Direction by the right-hand rule (CCW positive in 2D by handbook convention).

$M$ (N·m): Moment
$F$ (N): Force
$d$ (m): Perpendicular lever arm
$ϕ$: Angle between r and F

Step-by-step solved example

A 200 N force acts 1.5 m to the right of a bolt, perpendicular. Moment about the bolt?

M = Fd = Fr sinφ. Slide the force along its line of action.

1. Lever
d = 1.5 m (already perpendicular).
2. Moment
M = 200 × 1.5 = 300 N·m.
$M = 300 t e x t N \cdot m$

Answer: 300 N·m

10 practice questions

0/10 correct

1.If F is parallel to r (φ = 0), M =

2.Varignon’s theorem says the moment of a resultant equals

3.A couple’s moment is

4.50 N with lever 0.40 m perpendicular. M =

5.F = 10 N, r = 2 m, φ = 30°. |M| =

6.Sliding a force along its line of action

7.Right-hand rule: CCW in the page is

8.Moment units N·m are also

9.A force through point O has moment about O of

10.3D moment about an axis uses