Moments: Moment of a force about a point.

The idea

The moment of a force about a point is the turning effect of that force, calculated as the product of the force and the perpendicular distance from the point to the line of action of the force. The equation is M = F × d, where M is the moment in newton metres (N m), F is the force in newtons (N), and d is the perpendicular distance in metres (m). For example, a spanner of length 0.25 m with a force of 40 N applied perpendicular to the handle produces a moment of 10 N m about the nut. If the force is not perpendicular, resolve it into a component perpendicular to the lever arm, or use the perpendicular distance from the pivot to the line of action. Moments can be clockwise or anticlockwise, and for an object in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about any point.

What earns the marks

• State that the moment of a force is the product of the force and the perpendicular distance from the pivot to the line of action of the force.
• Use the equation M = F × d with correct units: force in N, distance in m, moment in N m.
• Identify the perpendicular distance correctly, which may require resolving a force or measuring perpendicular to the line of action.
• Determine the direction of the moment as clockwise or anticlockwise about the chosen point.
• Apply the principle of moments for equilibrium: sum of clockwise moments equals sum of anticlockwise moments about any point.
• Calculate an unknown force or distance using the principle of moments.

Common mistakes and how to put them right

• Using the distance along the lever rather than the perpendicular distance.

  Put it right by drawing the line of action and measuring the perpendicular distance from the pivot.

• Forgetting to convert distances from centimetres to metres.

  Put it right by converting to SI units before calculating.

• Adding moments in different directions without considering sign.

  Put it right by assigning clockwise and anticlockwise moments opposite signs or comparing their sums separately.

• Assuming the moment is the same regardless of the angle of the force.

  Put it right by resolving the force or using the perpendicular component.

Exam tips

• Always draw a diagram showing the pivot, the force, and the perpendicular distance to avoid errors.
• Check that the distance used is perpendicular to the force; if not, resolve the force into components.
• For equilibrium problems, take moments about a point to eliminate unknown forces that act through that point.
• Include units in your final answer and ensure they are correct for a moment (N m).