CENTER OF MASS

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CENTER OF MASS
IHSAN DOGRAMACI FOUNDATION BILKENT ERZURUM
LABORATORY HIGH SCHOOL
Cemre Çise KADIOGLU 102
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KEY WORDS
Center of gravity, plumb line
Weight, torque
Resultant-gravitional forces
Stability
Balance
Equilibrium
Turning effect
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What is centre of mass?

• The small forces act like a single force at G.
  This means that they have the resultant force at
  G.
• The resultant force is the sticks weight.
• G is the centre of mass.

Gravitional forces on particles of stick
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What is centre of mass?

• Centre of mass of a body is the body that moves
  as though all of the mass were applied there.

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Finding centre of mass

• If the object is uniform, for example a meter
  stick, the center of mass will be at the exact
  geometric center.
• But, if the shape is irregular we use plumb line.
• Draw lines from each vertex along the plumb line
  by assuming that the point is on that line
• After drawing the lines the centre of the mass
  will be on the intersection point of these lines.

G
Intersection point-Centre of mass
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Finding the centre of mass

• But, if the shape is irregular we use plumb line.
• Draw lines from each vertex along the plumb line
  by assuming that the point is on that line
• After drawing the lines the centre of the mass
  will be on the intersection point of these lines.

Intersection point-centre of mass
Plumb line
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• Balancing unequal masses are again about centre
  of mass
• For example,
• The bus is heavier than the car so theyre not in
  balance.

M2
M1
d2
d1
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• In order to balance the system, we should change
  their distances to the support.
• Now theyre in balance.

d1
d2
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Stability Equilibrium

• If an object isnt moving and remainig same, the
  object is stable.
• State of rest or balance due to the equal action
  of opposing forces is called equilibrium.
• When the object is stable its also in
  equilibrium which means the forces acting on the
  object and the forces turning effects are in
  balance.

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Stability-Equilibrium
Will turn to its original position
Small force will turn it over
Will definetely fall over before another force is
applied
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Types of equilibrium

• There are three states of equilibrium,

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Stable equilbrium

• The objects that have wide base also have the
  lower centre of mass.
• The lower the centre of mass is, the more stable
  object is.
• So its more difficult to fall over an object
  with wider base.

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Unstable equilibrium

• The objects that have very little base, have high
  centre of mass.
• And if these objects are tilted the centre of
  mass immediately passes beyond the base.
• So theyre not stable and its easy to fall these
  objects over.

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Neutral equilibrium

• The objects that are in neutral equilibrium stay
  where theyre lefted.
• When moved, it changes the position.
• Wherever they stay, their center of mass is
  always over their base.

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References

• Complete Physics for IGCSE
• http//dev.physicslab.org/Document.aspx?doctype3
  filenameRotaryMotion_CenterMass.xml
• http//dictionary.reference.com/browse/equilibrium
  
• http//en.wikipedia.org/wiki/Center_of_mass
• http//eteach.engr.wisc.edu/meibom/espp/slides/esp
  p.ppt
• http//solar.njit.edu/cdenker/physics111_lecture0
  8.ppt