The Moment Arm of an Inclined Force
Slant the force and the distance you measured along the bar stops being the arm. The perpendicular from the pivot down to the line of action is drawn in for you as d = L sin θ, and the panel works the moment out both ways — the whole force on a shortened arm, or the perpendicular component on the whole bar — so you can watch the two agree.
How to use this simulation
- Set the force, its distance along the bar and the angle between them
- Watch the perpendicular arm d = L sin θ redraw itself as you change the angle
- Load the worked example — 4.0 N at 60°, applied 4.0 m from A
- Press Along the bar to set θ = 0° and watch the moment die completely
What to look for
- The perpendicular arm is always shorter than the distance measured along the bar
- The whole-force-on-a-short-arm and component-on-the-full-bar routes agree exactly
- A force square to the bar at 90° uses the entire length as its arm and gives the largest moment
- At 0° the line of action runs through the pivot and the moment is zero
- Angles of θ and 180° − θ give identical moments, since both have the same sine
The physics behind it
A moment is the force times the perpendicular distance from the pivot to its line of action. When a force of size F acts at a point a distance L along the bar and at angle θ to it, that perpendicular distance is d = L sin θ, so M = F·L sin θ. Grouping the same product the other way, (F sin θ)·L, is the component method: only the part of the force perpendicular to the bar turns it, and the part along the bar pulls straight through the pivot and contributes nothing. Both groupings are the same product and must give the same moment.