🕛 Clockwise moment
The force tries to turn the object the same way that the hands of a clock move. Pushing down on the right-hand end of a see-saw gives a clockwise moment about the pivot in the middle.
Forces, Movement, Shape and Momentum » Moments and Centre of Gravity
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 1.30P, 1.31P, 1.2P
- What the moment of a force is and how to calculate it
- Why the distance must be the perpendicular distance from the pivot
- How to use the newton metre (Nm) and describe clockwise and anticlockwise moments
- That the weight of a body acts through its centre of gravity
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Unlock This CourseForces that turn things
This lesson is examined in Paper 2 only.
A force can make something turn. Push a door and it swings round its hinges. Pull on a spanner and the nut turns.
The fixed point that an object turns around is called the pivot. For a door, the pivot is the hinge. For a spanner, the pivot is the centre of the nut. The turning effect of a force about a pivot is called the moment of the force.
Try opening a door by pushing it close to the hinges. It is hard work. Push at the edge furthest from the hinges and it is easy. So a moment depends on two things: the size of the force and how far it is from the pivot.
Key terms:
- Pivot: the fixed point that an object turns around.
- Moment: the turning effect of a force about a pivot.
- Perpendicular distance: the distance from the pivot to the line of the force, measured at right angles (90°) to the force.
- Newton metre (Nm): the unit of a moment.
The moment equation
moment = force × perpendicular distance from the pivot
In symbols this is often written as M = F × d.
- force is in newtons (N)
- perpendicular distance from the pivot is in metres (m)
- moment is in newton metres (Nm)
This equation is not given in the exam, so you must learn it.
Worked example 1
A mechanic pulls on the end of a spanner with a force of 20 N. The force is at right angles to the spanner, 0.25 m from the centre of the nut. Calculate the moment of the force.
moment = force × perpendicular distance from the pivot
moment = 20 × 0.25
moment = 5 Nm
Worked example 2: change cm to m first
A boy pushes a door with a force of 12 N. He pushes at right angles to the door, 75 cm from the hinges. Calculate the moment of the force about the hinges.
75 cm = 0.75 m
moment = force × perpendicular distance from the pivot
moment = 12 × 0.75
moment = 9 Nm
Worked example 3: finding the force
A moment of 24 Nm is needed to undo a tight wheel nut. Calculate the force needed at the end of a spanner 0.30 m long. The force is at right angles to the spanner.
force = moment / perpendicular distance from the pivot
force = 24 / 0.30
force = 80 N
With a spanner twice as long (0.60 m), the force needed is 24 / 0.60 = 40 N, only half as much.
Why the distance must be perpendicular
The distance in the equation is the perpendicular distance: the shortest distance from the pivot to the line along which the force acts. It meets the line of the force at a right angle.
Picture a door seen from above, drawn as a straight line with the hinge at the left end. Draw three force arrows at the right end:
- Arrow at right angles to the door. The perpendicular distance is the full width of the door. This gives the biggest moment.
- Arrow at a slant to the door. Extend the arrow into a long straight line. The perpendicular distance from the hinge to this line is less than the width of the door, so the moment is smaller.
- Arrow pointing along the door, straight towards the hinge. The line of the force passes through the pivot. The perpendicular distance is zero, so the moment is zero.
In most exam questions the force is at right angles to the object, so the perpendicular distance is simply the distance along the object from the pivot to the force.
Clockwise and anticlockwise
A moment has a direction of turning. You describe it by comparing it with the hands of a clock.
🔄 Anticlockwise moment
The force tries to turn the object the opposite way to the hands of a clock. Pushing down on the left-hand end of the same see-saw gives an anticlockwise moment.
When you give a moment in an answer, give its size, its unit and its direction, for example "9 Nm clockwise".
Moments in everyday tools
Many tools give a large moment from a small force by putting your force a long way from the pivot.
🔧 Spanner
The pivot is the centre of the nut. A longer spanner gives a larger moment for the same pull, so a tight nut is easier to undo.
🚪 Door handle
The handle is fitted on the side of the door furthest from the hinges. This gives the largest perpendicular distance, so a small push opens the door.
🔨 Lever
A lever is a rigid bar that turns about a pivot. A claw hammer pulling out a nail is a lever. Your hand is far from the pivot, so your pull has a large moment.
Centre of gravity
Every tiny part of a body has weight, but you do not need thousands of small weight arrows. The weight of a body acts through a single point called its centre of gravity. You can treat the whole weight as one force acting at that point.
Key terms:
- Centre of gravity: the point through which the weight of a body acts.
- Uniform: the same all the way along, so the mass is spread evenly.
For a uniform body with a regular shape, the centre of gravity is at its centre:
- a uniform metre ruler: the middle, at the 50 cm mark
- a uniform rectangular sheet: where the two diagonals cross
- a uniform disc or a ball: the centre
When you draw the weight of a body, start the arrow at the centre of gravity and draw it straight down.
The weight of a body can have a moment of its own.
Worked example 4
A uniform metre ruler has a weight of 1.2 N. It is held horizontally with a pivot at the 0 cm end. Calculate the moment of its weight about the pivot.
The ruler is uniform, so its weight acts at the 50 cm mark. This is 0.50 m from the pivot.
moment = force × perpendicular distance from the pivot
moment = 1.2 × 0.50
moment = 0.60 Nm
Finding the centre of gravity of a flat card. For a card with an odd shape you can find the point by experiment. A plumb line is a string with a small weight on the end, so it always hangs straight down.
- Make a small hole near the edge of the card. Hang the card from a pin so that it can swing freely.
- Hang the plumb line from the same pin. Wait until the card and the string are still.
- Draw a line on the card along the string.
- Repeat with a hole in a different place on the card.
- The centre of gravity is where the lines cross.
This works because a card that hangs freely always comes to rest with its centre of gravity directly below the pin.
Common mistakes
- Leaving the distance in centimetres. Change centimetres to metres before you multiply, or your answer will be 100 times too big.
- Writing the unit as N/m. A moment is a force multiplied by a distance, so the unit is Nm.
- Using the wrong distance. It must be the perpendicular distance from the pivot to the line of the force, not just any length on the diagram.
- Drawing the weight arrow from the bottom or the end of an object. Weight acts through the centre of gravity.
Exam-style question
A cyclist pushes straight down on a bicycle pedal with a force of 300 N. The pedal is on the end of a metal arm called a crank. The crank is 17 cm long and turns about a pivot at its other end.
(a) State the formula linking moment, force and perpendicular distance from the pivot. [1 mark]
(b) The crank is horizontal. Calculate the moment of the 300 N force about the pivot. Give the unit. [3 marks]
(c) Later, the crank points straight down, with the pedal directly below the pivot. The cyclist still pushes straight down with 300 N. Explain why the moment of the force is now zero. [2 marks]
(d) The crank is a uniform metal bar. State where the centre of gravity of the crank is. [1 mark]
Model answer
(a) moment = force × perpendicular distance from the pivot (1)
(b) 17 cm = 0.17 m (1)
moment = 300 × 0.17 (1)
moment = 51 Nm (1)
(c) The line of the force passes through the pivot (1), so the perpendicular distance from the pivot is zero and force × 0 = 0 (1).
(d) In the middle of the crank, halfway along its length (1).
Exam tip
In part (b), one mark is for changing 17 cm into 0.17 m, so write that line down. An answer of 5100 would lose marks. In part (c), use the words "perpendicular distance" and "zero".