O-Level Physics Moments: Find the Perpendicular Distance First

Make the geometry visible before calculating

In a public SGExams Physics discussion, a candidate described a mistake when using Pythagoras to obtain a perpendicular distance for a moments calculation. The useful lesson is specific: recalling “force times distance” does not settle which distance belongs in the formula. This article uses original examples rather than attempting to reconstruct the examination diagram.

The 2026 SEAB O-Level Physics 6091 syllabus includes moments, the perpendicular-distance relationship and the principle of moments. Check your own subject and examination year when choosing papers, particularly when using these O-Level resources for another course.

Draw the force's line of action

Mark the pivot with a clear dot. Draw the force arrow where the force acts, then extend its direction as a straight line. The relevant distance is the shortest distance from the pivot to that line. Draw it meeting the line at a right angle. It may be different from the distance between the pivot and the point where the arrow touches the object.

Imagine a horizontal beam pivoted at its left end. A downward force acts at its right end. The force's line of action is vertical, so the horizontal length from the pivot to that line is perpendicular to it. Now imagine the force acts horizontally along the beam instead. Its line of action passes through the pivot, giving zero perpendicular distance and therefore zero moment about that pivot.

Work one straightforward example fully

Take an ideal light horizontal beam with a pivot between its ends. A 12 N downward force acts 0.30 m to the left of the pivot. A second downward force acts 0.20 m to the right. Suppose the beam is in equilibrium and no other forces produce moments about the pivot. The left force tends to turn the beam anticlockwise; the right force tends to turn it clockwise.

The anticlockwise moment is 12 × 0.30 = 3.6 N m. For balance, F × 0.20 = 3.6, giving F = 18 N. The larger force acts at the shorter distance. This provides a useful sense check before checking the arithmetic. The pivot's support force produces no moment about that pivot because its line of action passes through it.

The “light beam” assumption matters. If the question gives the beam's weight, include its moment at the stated centre of gravity. Equal clockwise and anticlockwise moments address rotational balance; do not treat that alone as proof that every force on an object is balanced. Read what the problem actually asks.

When a triangle appears, identify its sides

For an original geometry check, suppose the pivot is 0.50 m from the point where a force is applied. On the force's extended line of action, that application point is 0.30 m from the foot of the perpendicular dropped from the pivot. These three points form a right triangle. The 0.50 m side is the hypotenuse; the moment arm is the other short side.

Consequently, d² = 0.50² − 0.30² = 0.16 and d = 0.40 m. A 15 N force acting along that line has moment 15 × 0.40 = 6.0 N m. Adding the two squares would give a distance longer than the hypotenuse, warning you that the geometry has been misread. Do not apply Pythagoras until the right angle and hypotenuse are identified.

Keep distances, units and directions together

If a distance is given as 40 cm, convert it to 0.40 m before reporting a moment in N m. If a load is supplied as a mass, calculate its weight using the gravitational field strength provided or required by that question. A mass in kilograms is not already a force in newtons. Label each moment's clockwise or anticlockwise direction before setting up an equation.

Choose practice that tests the diagram

From the TestPapersFree Pure Physics collection, select a few turning-effects questions. For each, mark the pivot, force lines and right angles before using numbers. After checking, classify any mistake as geometry, omitted force, turning direction, conversion or arithmetic. Redraw a missed diagram without its values and explain which distance matters. That explanation is a more useful next step than repeating the same wrong calculation faster.