Moment defined as force × perpendicular distance from the point to the…

The idea

A moment measures the turning effect of a force about a chosen point. To calculate it, multiply the force by the perpendicular distance from that point to the force's line of action. The line of action is the infinite straight line along which the force acts. If the force is not perpendicular to the line joining the point to the force, resolve the force into a component perpendicular to that line, or find the perpendicular distance from the point to the line of action. For example, a 20 N force applied at the end of a spanner 0.25 m from a nut, perpendicular to the spanner, gives a moment of 20 N × 0.25 m = 5.0 N m about the nut. The unit is the newton metre (N m), not the joule, because the distance is perpendicular to the force.

What earns the marks

• State that the moment of a force about a point equals the product of the force and the perpendicular distance from the point to the line of action of the force.
• Identify the line of action as the straight line through the point of application along the direction of the force.
• Use the perpendicular distance, not the distance along the force or the direct distance to the point of application unless that distance is perpendicular.
• Calculate moments using moment = F × d with consistent units, giving the unit N m.
• Resolve a force into a component perpendicular to a chosen line when the force is not already perpendicular to it.
• Recognise that the moment depends on the chosen point and increases with perpendicular distance for a given force.

Common mistakes and how to put them right

• Using the direct distance from the pivot to the point of application instead of the perpendicular distance to the line of action.

  Put it right by drawing the line of action and dropping a perpendicular from the pivot to it.

• Treating the moment unit as the joule.

  Put it right by writing N m, because moment is not energy.

• Forgetting to resolve a force that acts at an angle.

  Put it right by using the perpendicular component F sin θ or F cos θ as appropriate to the geometry.

• Adding distances along the force direction rather than measuring perpendicular distance.

  Put it right by identifying the perpendicular distance from the pivot to the line of action.

Exam tips

• Sketch the force, its line of action and the perpendicular distance before substituting numbers into moment = F × d.
• Check that the distance is perpendicular to the force; if not, resolve the force or find the perpendicular distance.
• Give the unit as N m and keep the direction of turning (clockwise or anticlockwise) clear when several moments act.