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Balanced and unbalanced forces
When forces in opposite directions have the same value,
they cancel each other out. The forces are balanced.
The object is either stationary or moves at a constant speed.
If the forces on an object are not balanced, there is a
resultant force, and the object accelerates in the direction
of this force.
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Turning effects from balanced forces
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Examples of turning effects
These are some examples of everyday turning effects:
Can you think of any more?
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What is a moment?
A moment矩 is a turning effect caused by a force.
The size of the turning effect
caused by a force depends on two
factors. What are they?
The bigger the force, the larger
the turning effect.
The larger the perpendicular 垂
直distance from the pivot 中心点
to the point where the force is
applied, the larger the turning
effect.
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The moment equation
The size of a moment obeys the moment equation:
moment (Nm) = force (N) × perpendicular distance
from pivot (m)
In this example, the forces are constant, but the larger the
perpendicular distance, the faster the roundabout
accelerates:
force
perpendicular
distance
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Perpendicular distances
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Clockwise and anticlockwise moments
When Mark and Tim lift their feet off the ground, what will
happen to the see-saw?
Tim
Mark
The force of gravity creates a turning effect on each person.
On the left-hand side, it creates an anticlockwise moment.
On the right-hand side, it creates a clockwise moment.
The clockwise moment is larger than the anticlockwise
moment, so the see-saw will turn in a clockwise direction.
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The principle of moments
If an object is balanced about a pivot, then we can say that:
sum of anticlockwise
moments
=
sum of clockwise
moments
This is the principle of moments.
So, the forces on an object must obey two conditions to keep
the object completely stationary:
1. The forces must be balanced.
2. The moments must be balanced.
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Using the principle of moments
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What is a centre of mass?
Can you balance a ruler on the flat end of a pencil?
If so, where do you put the pencil to make it balance?
The ruler is stationary when
the moments from the weights
of its entire length balance out.
This is equivalent to one weight
force acting through the centre of
the ruler.
The point at which all the mass of an object seems to be
concentrated is called its centre of mass.
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Forces and centres of mass
How can the idea of centre of mass help us to understand
this statement?
“When the forces on an object are
balanced, it is either stationary or
moves at a constant speed.”
What does ‘stationary’ mean if an
object is turning?
When forces on an object are
balanced, its centre of mass
is stationary, or moves at a
constant speed.
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Centre of mass or centre of gravity?
Imagine that the gravitational field on the left of this picture
suddenly becomes much stronger than the gravitational field
on the right. Would the see-saw still balance?
The see-saw’s centre of mass is still in the centre of the
picture. But its centre of gravity – the point where all its
weight appears to act – has moved to the left.
In a uniform gravitational field, such as on the Earth’s surface,
centre of gravity is equivalent to centre of mass.
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Finding a centre of mass
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Finding a centre of mass
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Understanding centres of mass
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When is an object stable?
An object is said to be in stable equilibrium if it returns to
its original position when it is disturbed.
This happens because its centre of mass moves upwards
when pushed, so gravity tends to pull the object back down
towards its equilibrium position.
An object is in stable
equilibrium if its
centre of mass is
suspended below a
pivot, or balanced
above a wide base.
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C.O.M.
When is an object unstable?
An object is said to be in unstable equilibrium if it falls or
topples when it is disturbed.
This happens because its centre of mass moves downwards
when pushed, so gravity tends to pull the object further away
from its equilibrium position.
An object is in unstable
equilibrium if its centre of
mass is balanced above a
pivot point or a narrow base.
C.O.M.
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Stable or unstable?
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Neutral equilibrium
An object is said to be in neutral equilibrium if it moves
sideways when it is disturbed.
This happens because its centre of mass stays at the same
height when pushed, so gravity does not tend to pull the
object towards or away from its original position.
Spheres and cylinders are
examples of objects that can
be in neutral equilibrium
when resting on flat ground.
C.O.M.
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Recognizing states of equilibrium
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Losing equilibrium
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Making things more stable
Look at the picture to the
right. Can you explain
why this situation is
dangerous, using ideas
about centre of mass and
stable and unstable
equilibrium?
How could you make the
bus more stable?
Think of two solutions.
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Understanding stability
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Glossary
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Anagrams slide
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Multiple-choice quiz
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