Download Moments and Centre of Gravity

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Introduction to turning forces
Forces can make things accelerate. They can also make
things rotate.
What’s wrong with these pictures?
too
short!
too
short!
wrong
place!
We know instinctively that we need to apply a force at a large
distance from the pivot for it to be effective.
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Moments and torque
A moment is the turning effect of a force. It can also be
called a torque. Torque is given the symbol t (the Greek
letter tau). Its units are newton metres (Nm).
pivot
F
d
F – the force applied in newtons (N).
d – the perpendicular distance (in m) between the pivot
and the line of action of the force.
t=F×d
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Moments for non-perpendicular distance
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Couples and torques
A couple is a pair of forces acting on a body that are of
equal magnitude and opposite direction, acting parallel
to one another, but not along the same line.
Forces acting in this way produce a turning force or moment.
The torque of a couple is the rotation force or
moment produced.
F
d
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F
The forces on this beam are
a couple, producing a
moment or torque, which will
cause the beam to rotate.
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The torque of a couple
There is a formula specifically for finding the torque of a couple.
A point P is chosen arbitrarily.
Take moments about P.
F
P
d–x
x
d
total moment = Fx + F(d – x)
F
= Fx + Fd – Fx
= Fd
perpendicular distance
torque of a couple = force × between lines of action
of the forces
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Moments: testing
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Centres of mass and gravity
The centre of gravity of an object is a point where the
entire weight of the object seems to act.
The centre of mass of an object is a point where the
entire mass of the object seems to be concentrated.
In a uniform gravitational field the centre of mass is in the
same place as the centre of gravity.
An alternative definition is that the centre of mass or centre of
gravity of an object is the point through which a single force
has no turning effect on the body.
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Finding the centre of gravity
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Centre of gravity: testing
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Equilibrium
A body persists in equilibrium if no net force or
moment acts on it. Forces and moments are balanced.
Newton’s first law states that a body persists in its state of
rest or of uniform motion unless acted upon by an external
unbalanced force.
Bodies in equilibrium are therefore bodies that are at rest or
moving at constant velocity (uniform motion).
F1
F2
F2
F1
equilibrium
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Balanced moments
If the total clockwise moment on an object is balanced by the
total anticlockwise moment, then the object will not rotate.
Provided that there are no other unbalanced forces on it, the
object will be in equilibrium, like the beam below:
4m
3N
2m
6N
total anticlockwise moments = total clockwise moments
3×4=6×2
12 Nm = 12 Nm
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The principle of moments
The principle of moments states that (for a body in
equilibrium):
total clockwise
moments
=
total anticlockwise
moments
This principle can be used in calculations:
5m
What is d?
d
4 × 5 = 6d
4N
6N
20 = 6d
d = 20 / 6
d = 3.3 m
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Can you make the beam balance?
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Balancing moments calculations
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Human forearm
The principle of moments can
be used to find out the force,
F, that the biceps need to
apply to the forearm in order to
carry a certain weight. When
the weight is held static, the
system is in equilibrium.
Taking moments about
the elbow joint:
4F = (16 × 20) + (35 × 60)
4F = 2420
weight of arm = 20 N
60 N
4 cm
F
schematic diagram
16 cm
20 N
35 cm
60 N
F = 605 N
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Centre of gravity and equilibrium
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Finding the weight of a metre rule
The uniform metre rule shown is in equilibrium, with its centre
of gravity marked by the arrow ‘weight’. Find the weight of the
metre rule.
0.2 m
3N
0.3 m
0.5 m
W
total anticlockwise moments = total clockwise moments
3 × 0.2 = weight × 0.3
weight = 0.6 / 0.3
weight = 2 N
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Equilibrium: testing
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Glossary
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What’s the keyword?
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Multiple-choice quiz
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