Lesson 1 of 4
Moments and perpendicular distance
I can describe a force's turning effect about a pivot and relate it to everyday examples.Syllabus
Syllabus K323, 4(a). Describe a force's turning effect about a pivot and relate it to everyday examples.
I can apply moment = force x perpendicular distance to new situations.Syllabus
Syllabus K323, 4(b). Apply moment = force x perpendicular distance to new situations.
Make a guess. You are not marked.
You push a door with the same force at two places: close to the hinge, and at the handle on the far edge. Which push turns the door more easily?
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The push at the handle.
The moment is force times perpendicular distance from the pivot. The handle is far from the hinge, so the same force gives a much larger turning effect there.
The moment of a force describes its turning effect about a pivot. A force can have a turning effect even if other forces prevent the object from rotating.
A door turns about its hinges. A spanner turns about the centre of a nut. The pivot is the point or axis about which we consider the turning. For a given force, pushing farther from the pivot can produce a larger moment.
Use force in newtons and distance in metres. A force is different from a mass; review forces and weight or unit conversions if needed.
Moment = F x dF is the force in N. d is the perpendicular distance in m from the pivot to the force's line of action. The moment is measured in newton metres, N m.
A moment is also called a torque. State its turning sense: clockwise or anticlockwise in the view being used. N m means force multiplied by distance; N/m is not the unit of moment.
The same push at different distances
Imagine a 12 N push perpendicular to a door. At 0.75 m from the hinge, its moment is 12 x 0.75 = 9.0 N m. At 0.25 m, the same perpendicular push gives 12 x 0.25 = 3.0 N m.
The farther push has three times the turning effect because its perpendicular distance is three times as large. This explains why a door handle is usually placed far from the hinge and why a longer spanner can make a nut easier to turn.
The line of action determines the distance
The line of action is the straight line along which the force acts. Imagine extending the force arrow straight in both directions. Measure the shortest distance from the pivot to that line: it must meet the line at a right angle.
Measure to the force's line of action
Moment = 12 x 0.40 = 4.8 N m clockwise.
Dashed lines are construction guides. The blue curve shows turning sense, not an extra force.
A force through the pivot has zero moment
Perpendicular distance = 0. Moment about O = 0 N m.
Worked example
A tilted handle
Point A is 0.40 m to the right and 0.30 m above pivot O. The handle OA is 0.50 m long. A 12 N force acts vertically downwards at A.
- Identify the line of action: it is vertical through A.
- Select the perpendicular distance: the horizontal distance from O to that line is 0.40 m.
- Calculate: moment = 12 x 0.40 = 4.8 N m.
- Give the turning sense: a downward force to the right of O turns the handle clockwise in this view.
Using 12 x 0.50 would give 6.0 N m, but the handle's length is not the required perpendicular distance. The curved turning arrow indicates a sense of rotation; it is not another force.
A force can have zero moment
If the force at A is directed along the handle towards O, its line of action passes through the pivot. The perpendicular distance is zero, so its moment about O is zero. The force still exists; it simply has no turning effect about that point.
Worked example
Find a force from a required moment
A perpendicular lever arm is 0.20 m. What force gives a moment of 4.8 N m?
F = moment / d = 4.8 N m / 0.20 m = 24 N
The metre units cancel, leaving newtons. If the force is given and the lever arm is unknown, rearrange to d = moment / F.
Try it step by step
Work it out in steps: Perpendicular distance in m, then Moment = F x d in N m.
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Problem 1.
Perpendicular distance in m: d = 40 cm = 0.40 m
Moment = F x d in N m: Moment = 15 x 0.40 = 6.0 N m (2 sf)
Problem 2.
Perpendicular distance in m: d = 60 cm = 0.60 m
Moment = F x d in N m: Moment = 25 x 0.60 = 15 N m (2 sf)
Problem 3.
Perpendicular distance in m: d = 25 cm = 0.25 m
Moment = F x d in N m: Moment = 8.0 x 0.25 = 2.0 N m (2 sf)
Choose the distance before multiplying. It is not automatically the length of the handle or the distance to the point where the force is applied. Locate the line of action and its perpendicular from the pivot.
Check your understanding
Viewed from the front, a 10 N force acts vertically downwards at a point to the right of a pivot. The handle is 0.50 m long, but the perpendicular distance from the pivot to the force's line of action is 0.30 m. What is the moment?
Show the answer
3.0 N m clockwise.
Moment = force x perpendicular distance = 10 x 0.30 = 3.0 N m. A downward force on the right tends to turn the body clockwise in the stated view.
Practise an exam question
Write your answer first, then tick the mark points it makes.
Exam-style question
Define the moment of a force. A mechanic pushes at right angles on the end of a spanner 0.20 m from the centre of a nut with a force of 25 N. Calculate the moment of the force about the nut. [3]
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