Center of Gravity

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Center of Gravity

• Unit 6

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Center of gravity- the point on an object located
at the objects average position of weight

• Symmetrical object (baseball)- CG is at the
  geometric center
• Irregularly shaped object (baseball bat)- CG is
  towards the heavier end

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Objects not made of the same material throughout
may have the center of gravity quite far from the
geometric center.
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If a wrench were slid along a straight path, the
CG follows a straight-line path. Other parts of
the wrench rotate about this point as the wrench
moves across the surface.
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Center of gravity is often called center of mass,
which is the average position of all particles of
mass that make up an object.
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Measuring center of gravity

• The CG of a uniform object (such as a meter
  stick) is at the midpoint, its geometric center.
  The CG is the balance point. Supporting that
  single point supports the whole object.

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Measuring center of gravity

• If you suspend any object (for ex, a pendulum) at
  single point, the CG of the object will hang
  directly below the point of suspension. To locate
  the CG, construct a vertical line beneath the
  point. The CG lies somewhere along that line. You
  can locate the CG by suspending the object from
  some other point and constructing a second
  vertical line. The CG is where the two lines
  intersect.

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The CG of an object may be located where no
actual material exists (for example, a rings CG
is the hollow center).
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Look at the picture below. You can see that the
block will begin to topple when the plumb line
extends beyond the supporting base of the block.
The rule is this if the CG is above the area of
support, the object will remain upright. If the
CG extends outside the area of support, the
object will topple. This explains why the
Leaning Tower of Pisa does not topple its CG
does not extend beyond its base.
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Consider a solid wooden cone on a level table.
You cannot stand it on its tip. Even if you
position it so that its CG is exactly above its
tip, the slightest vibration will cause the cone
to topple.However, a cone balances easily on
its base.
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An object balanced so that any displacement
lowers its CG is in unstable equilibrium.An
object that is balanced so that any displacement
raises its CG is in stable equilibrium.An
object placed in a position where the CG is
neither raised nor lowered is in neutral
equilibrium.
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The CG of a building is lowered if most of the
structure is below ground level. This structure
is so deeply rooted that its CG is actually
below ground level making it very stable.
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When you stand erect with your arms hanging at
your sides, your CG is within your body. It is
typically 2 to 3 cm below your navel, and midway
between your front and back. The CG is slightly
lower in women than in men because women tend to
be proportionally larger in the pelvis and
smaller in the shoulders. In children, the CG is
approximately 5 higher because of the
proportionally larger heads and shorter legs.
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When you stand, your CG is somewhere above your
support base, the area bounded by your feet. In
unstable situations, as in standing in the aisle
of a bumpy-riding bus, you place your feet
farther apart to increase this area.
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