Mechanical Equilibrium
We are now ready to consider objects in equilibrium.
There are two
conditions to equilibrium for most objects.
The first condition is stated by
Newton's first law:
F
=
∑
0
The second condition of equilibrium is
τ
=
∑
0
Basically, we say that a body is in equilibrium if the vector sum of the forces and
torques are zero.
Usually, we will need to look at both translational equilibrium and rotational
equilibrium.
The rule of thumb is that if the body is a point source, or all of the
forces act at the same point on the body, then we do not need to consider
rotational equilibrium.
If the forces act at different points on the body, then we
must take rotation into account.
Center of Mass
In order to simplify our calculations, it is convenient to talk in terms of the
center of mass, or center of gravity, of a body.
We define the center of mass to
be the weighed average of the components of the body
X
m x
m
m x
M
CM
i
i
i
i
i
=
=
∑
∑
∑
(9.1)
If the object is a continuous mass distribution, we replace the summation with an
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 Spring '09
 Knott
 Physics, Equilibrium, Center Of Mass, Mass

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