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Edexcel IGCSE Physics Your notes
1.4 Moments
Contents
1.4.1 Moments
1.4.2 The Principle of Moments
1.4.3 Centre of Gravity
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1.4.1 Moments
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The Moment of a Force
As well as causing objects to speed up, slow down, change direction and deform, forces can also
cause objects to rotate
An example of a rotation caused by a force is on one side of a pivot (a fixed point that the object can
rotate around)
This rotation can be clockwise or anticlockwise
The force will cause the object to rotate clockwise about the pivot
A moment is defined as:
The turning effect of a force about a pivot
The size of a moment is defined by the equation:
M=F×d
Where:
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M = moment in newton metres (Nm)
F = force in newtons (N)
d = perpendicular distance of the force to the pivot in metres (m) Your notes
The moment depends on the force and perpendicular distance to the pivot
This is why, for example, the door handle is placed on the opposite side to the hinge
This means for a given force, the perpendicular distance from the pivot (the hinge) is larger
This creates a larger moment (turning effect) to make it easier to open the door
Opening a door with a handle close to the pivot would be much harder, and would require a lot more
force
Exam Tip
The unit of a moment is Newton metres (N m), but can also be Newton centimetres (N cm) ie. where the
distance is measured in cm insteadIf the exam question doesn't ask for a specific unit, always convert
the distance into metres
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1.4.2 The Principle of Moments
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The Principle of Moments
The principle of moments states that:
If an object is balanced, the total clockwise moment about a pivot equals the total
anticlockwise moment about that pivot
Remember that the moment = force × distance from a pivot
The forces should be perpendicular to the distance from the pivot
For example, on a horizontal beam, the forces which will cause a moment are those directed
upwards or downwards
Moments on a balanced beam
In the above diagram:
Force F2 is supplying a clockwise moment;
Forces F1 and F3 are supplying anticlockwise moments
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Due to the principle of moments, if the beam is balanced
Total clockwise moments = Total anticlockwise moments Your notes
Hence:
F 2 × d 2 = ( F 1 × d 1 ) + ( F 3 × d 3)
Worked example
A parent and child are at opposite ends of a playground see-saw. The parent weighs 690 N and the
child weighs 140 N. The adult sits 0.3 m from the pivot.
Calculate the distance the child must sit from the pivot for the see-saw to be balanced.
Step 1: List the know quantities
Clockwise force (child), Fchild = 140 N
Anticlockwise force (adult), Fadult = 690 N
Distance of adult from the pivot, dadult = 0.3 m
Step 2: Write down the relevant equation
Moment = force × distance from pivot
For the see-saw to balance, the principle of moments states that
Total clockwise moments = Total anticlockwise moments
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Step 3: Calculate the total clockwise moments
The clockwise moment is from the child Your notes
Momentchild = Fchild × dchild = 140 × dchild
Step 4: Calculate the total anticlockwise moments
The anticlockwise moment is from the adult
Momentadult = Fadult × dadult = 690 × 0.3 = 207 Nm
Step 5: Substitute into the principle of moments equation
140 × dchild = 207
Step 6: Rearrange for the distance of the child from the pivot
dchild = 207 ÷ 140 = 1.48 m
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Exam Tip
Your notes
Make sure that all the distances are in the same units and you’re considering the correct forces as
clockwise or anticlockwise, as seen in the diagram below
Clockwise is defined as the direction the hands of a clock move (and anticlockwise as the opposite)
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Your notes
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Supporting a Beam
A light beam is one that can be treated as though it has no mass Your notes
The supports, therefore, must supply upwards forces that balance the weight of any object placed on
the beam
F1 and F2 upwards balance the weight of the beam downwards
As the mass in the above diagram is moved from the left-hand side to the right-hand side of the beam,
force F1 will decrease and force F2 will increase
F1 decreases F2 increases keep the beam balanced
Consider what would happen to the beam if the right-hand support was removed:
Force F2 would be 0
The weight of the object would supply a moment about the left-hand support, causing the beam
to pivot in a clockwise direction
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Your notes
When F2 is removed the beam will rotate by the clockwise moment
Therefore, the force F2 must therefore supply an anticlockwise moment about the left-hand support,
which balances the moment supplied by the object
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1.4.3 Centre of Gravity
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Centre of Gravity
The centre of gravity of an object (sometimes called the centre of mass) is defined as:
The point through which the weight of an object acts
For a symmetrical object of uniform density, the centre of gravity is located at the point of symmetry
For example, the centre of gravity of a sphere is at the centre
The centre of gravity of a regular shape can be found by symmetry
The centre of gravity of an irregular object can be found by locating its balance point
A broomstick has a centre of gravity slightly closer to the head of the broom since there is more
mass located there
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Your notes
The centre of mass of a broomstick which is also its balance point
Exam Tip
Since the centre of gravity is a hypothetical point, it can lie inside or outside of a body. The centre of
gravity will constantly shift depending on the shape of a body. For example, a human body’s centre of
gravity is lower when learning forward than when stood uprightHowever, make sure that when you are
drawing force diagrams to draw the forces as if they were acting on the centre of gravity of the object!
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