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The
torque
τ
of a
force
has a magnitude that is given by the magnitude
F
of the force
times the lever arm
:
=
F
. The lever arm is the perpendicular distance between the
line of action of the force and the axis of rotation.
A rigid body is in
equilibrium
if it has zero translational
acceleration
and zero
angular acceleration
, so the net external
force
and the net external
torque
acting on the
body are zero. For forces acting only in the
x
,
y
plane, the conditions for equilibrium are
.
The
center of gravity
of a rigid object is the point where its entire
weight
can be
considered to act when calculating the
torque
due to the weight. For a symmetrical body
with uniformly distributed weight, the
center of gravity
is at the geometrical center of the
body. When a number of objects whose weights
W
1
,
W
2
, . . . are distributed along the
x
axis at locations
x
1
,
x
2
, . . . , the center of
gravity
is located at
x
cg
= (
W
1
x
1
+
W
2
x
2
+ . . . )/
(
W
1
+
W
2
+ . . . ). The
center of mass
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 Spring '08
 Sharp
 Force

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