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Moments

01Moments

Moment of a force

This section covers the turning effect of a force and calculating a moment using the perpendicular distance to its line of action.

Turning effect

A moment describes the turning effect produced by a force about a point or pivot.

The magnitude of the moment depends on the force and the perpendicular distance from the point to the force's line of action:

M=FdM=Fd

where MM is the moment, FF is the force and dd is the perpendicular distance from the point to the line of action of the force.

The SI unit of moment is the newton metre, N m. If a distance is supplied in another unit, it must be treated consistently in the calculation.

Fdpivotline of action

The distance used in M=FdM=Fd is not simply the distance from the pivot to where the force is applied. It must be measured perpendicular to the line of action of the force.

This is why increasing the perpendicular distance increases the turning effect for the same force. A door handle, for example, is positioned far from the hinge so that a smaller applied force can produce a useful moment.

If the applied force is not perpendicular to the lever, either identify the perpendicular distance to its line of action or resolve the force to obtain the component that acts perpendicular to the lever.

Worked example: A uniform metre rule is pivoted at the 50 cm50\,\text{cm} mark. A 0.50 kg0.50\,\text{kg} mass hangs from the 80 cm80\,\text{cm} mark. Neglect the weight of the rule. Find the moment produced by the hanging mass about the pivot.

The force is the weight of the mass:

F=mg=0.50×9.81=4.9 NF=mg=0.50\times9.81=4.9\,\text{N}

The perpendicular distance from the pivot is:

d=80−50=30 cm=0.30 md=80-50=30\,\text{cm}=0.30\,\text{m}

Therefore:

M=Fd=4.9×0.30=1.5 N mM=Fd=4.9\times0.30=1.5\,\text{N m}

Exam Tip: Before using M=FdM=Fd, mark the pivot and the force's line of action on the diagram. Use the shortest distance between them, because that is the perpendicular distance required in the equation.

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