Center of Gravity

1
Chapter 10

• Center of Gravity

2
Center of Gravity

• Center of Gravity the point located at an
  objects average position of weight
• At the geometric center of symmetrical objects
• Towards the heavier end of asymmetrical objects
  and objects with varying density
• CG follows the proper physical path of an object
• If an object is slide across a surface, the CG
  follows a straight line path
• If an object is thrown into the air, the CG
  follows a parabolic path

3
Center of Mass

• Center of Mass the average position of all the
  particles of mass that make up an object
• For most objects on/near the Earth-CG and CM are
  the same
• If an object is large enough for gravity to vary
  from one part to another, there may be a
  difference in CG and CM
• Skyscrapers can have a CG 1 mm below its CM
• The center of mass of the solar system is not at
  the geometric center of the solar system, the sun
  
• This is because all of the planets masses are
  taken into account for the center of mass
• This causes the sun to wobble as the planets
  orbit

4
Locating the CG

• The CG may be located where no actual material
  exists (outside an object)
• The CG is the balance point
• In a uniform object, it is the geometric center
• Where is the CG of a donut?
• Can an object have more than one CG?

5
Toppling

• If the CG of an object is above the area of
  support, the object will remain upright
• If the CG of an object is outside the area of
  support, the object will topple
• Will it topple?

6
Stability

• Equilibrium is
• unstable when the CG is lowered with displacement
• stable when work must be done to raise the CG
• neutral when displacement neither raises or
  lowers the CG
• The CG has the tendency to take the lowest
  position available
• The CG of a glass of ice water lowers when the
  ice cubes are floating at the top
• Shake a box of different size objects, the
  smaller objects slip into the spaces between the
  larger objects. This produces a greater
  effective density of spacelowering the CG

7
CG of People

• The CG of a person is not located in a fixed
  place, but depends on body orientation
• Raising your arms, raises your CG
• When you stand your CG is located above your
  support base (the area bounded by your feet)
• What can you do to increase your stability?
• Decrease stability?
• What happens to your CG if you touch your toes
  without bending your knees?
• Can you touch your toes without bending your
  knees (or falling) if the back of your feet are
  against the wall?