In a moment = force × distance calculation, the distance must be measured at a right angle to the line of the force. Checking this one step catches many wrong answers early.
This lesson sharpens the formula from calculating a moment and finishes moments and stability.
Why does the distance have to be perpendicular?
A force turns an object most effectively when it pushes at right angles to the arm. If it pushes partly along the arm, that part pulls or pushes towards the pivot and does not turn anything.
The perpendicular distance captures only the useful part. Draw the line of action of the force, extend it in both directions, then measure the shortest distance from the pivot to that line.
How do you check it on a diagram?
- Mark the pivot and draw the force arrow.
- Extend the force line through the arrow in both directions.
- Drop a line from the pivot to the force line so it meets at 90°.
- Measure or calculate that length. This is d.
- Ask whether it is plausible: d can never be longer than the straight line from the pivot to where the force is applied.
Worked example
A bar is pivoted at one end.
A 40 N force acts at a point on the bar that is 0.50 m from the pivot, but the force is not at right angles to the bar.
The perpendicular from the pivot to the force’s line of action is 0.30 m long. Its foot is 0.40 m along that line from the point where the force is applied. Find the moment.
Step 1, identify the triangle: the sides are 0.30 m (the perpendicular), 0.40 m (along the force line) and 0.50 m (along the bar). This is a 3-4-5 right triangle scaled by 0.1, so the lengths are consistent: 0.30² + 0.40² = 0.09 + 0.16 = 0.25 = 0.50².
Step 2, choose d: the perpendicular distance is 0.30 m, not 0.50 m.
Step 3, multiply: 40 × 0.30 = 12 N m.
Answer: 12 N m.
If the angle θ between the force line and the bar is given instead, d = 0.50 × sin θ. Here sin θ = 0.30 ÷ 0.50 = 0.60, so the same result follows.
The mistake to watch for
A common slip is to use the length of the bar as the distance, whatever the direction of the force.
Mistaken working: 40 × 0.50 = 20 N m.
The 0.50 m is along the bar. The force does not act at right angles to it, so the turning distance is shorter.
The correction is to draw the perpendicular from the pivot to the force line and use that length. The mistaken answer of 20 N m is too large, which is typical: using the bar length overstates the moment.
Check yourself
1. A 30 N force acts along a line that passes exactly through the pivot. What is its moment about the pivot?
Show answer
The perpendicular distance is 0, so the moment is 30 × 0 = 0 N m.
2. A door is 0.90 m wide. A person pushes at its edge at right angles with 10 N. Then the person pushes at the same point with 10 N, but the force makes 30° with the door surface. Find both moments about the hinge. (sin 30° = 0.5)
Show answer
Right angle: 10 × 0.90 = 9.0 N m. At 30°: d = 0.90 × sin 30° = 0.45 m, so moment = 10 × 0.45 = 4.5 N m. The slanted push has half the turning effect.
3. A bar is 0.50 m long from the pivot to the point of application. The perpendicular distance from the pivot to a 25 N force line is 0.30 m. Find the moment.
Show answer
Use the perpendicular distance: 25 × 0.30 = 7.5 N m. Using 0.50 m would wrongly give 12.5 N m.
Where this leads next
Put all five lessons together in the moments and stability practice set. The triangle and bearings reasoning board also helps you practise choosing the right triangle before calculating.
If you understand the idea but find it hard to spot the right distance on unfamiliar diagrams, the practice in online one-to-one Physics tuition can focus on that one habit.