S: Moments: Understand and use moments in simple static contexts.

The idea

A moment measures the turning effect of a force about a point. For a force F acting perpendicular to a rod at distance d from the pivot, the moment is F × d, measured in newton-metres (N m). In simple static contexts a rigid body is in equilibrium, so the total clockwise moment about any point equals the total anticlockwise moment. To solve a problem, choose a pivot to eliminate an unknown force, resolve perpendicular components where the force is not at right angles, and form an equation. For example, a uniform beam of weight 200 N resting on two supports: taking moments about one support gives the reaction at the other. Always state the pivot and check units and directions.

What earns the marks

• State the pivot point and confirm the body is in equilibrium before forming an equation.
• Use moment = force × perpendicular distance from the pivot, converting lengths to metres and forces to newtons.
• For a force at an angle, use the perpendicular component F sin θ or the perpendicular distance, not the full force along the rod.
• Take moments about a point to eliminate an unknown reaction or tension, then solve the resulting linear equation.
• Include the weight of a uniform rod as acting at its midpoint, and model a non-uniform rod by placing its weight at the centre of mass.
• Check the answer by taking moments about a second point or by resolving vertically.

Common mistakes and how to put them right

• Using the full force when it acts at an angle to the rod.

  Put it right by using the perpendicular component F sin θ or the perpendicular distance.

• Forgetting the weight of the beam or assuming it acts at the end.

  Put it right by placing the weight at the midpoint for a uniform beam.

• Mixing units, such as centimetres with newtons.

  Put it right by converting all lengths to metres before calculating moments.

• Adding moments on the same side of the pivot instead of equating clockwise and anticlockwise totals.

  Put it right by labelling each moment's direction.

Exam tips

• Draw a clear diagram, mark the pivot and label every force with its distance from the pivot.
• Choose the pivot at a point where an unknown force acts so that its moment is zero and disappears from the equation.
• Show the moment equation before solving, and give the final answer with correct units and a sensible direction.
• If a rod is on the point of tilting, set the reaction at the lifting support to zero before taking moments.