EFFECT OF CENTRIFUGAL AND CORIOLIS FORCES DUE TO EARTH

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EFFECT OF CENTRIFUGAL AND CORIOLIS FORCES DUE TO
EARTHS ROTATION ON g
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Effect of centrifugal force

• The acceleration of a particle in frame of
  reference S rotating with a constant angular
  velocity ? is given by
• 
  .(1)
• Here r is position vector of the particle and the
  other terms have their usual meaning.

When a particle is at rest on the surface of
earth which rotates
with constant angular velocity ? about its polar
axis, then
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• Then, Coriolis acceleration0
• i.e.
• and

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• Therefore, from equation (1),
• the acceleration is given by
• 
  (2)

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• Acceleration due to gravity at P acts along
  PO. The components of g are

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This acceleration is given by eqn. (2) as

• where ? is latitude of particle P.

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This equation shows that centrifugal acceleration
decreases the effective acceleration due to
gravity.
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• Hence
• there is no effect of rotation of earth on the
  value of acceleration due to gravity at its poles
• there is maximum effect of rotation of earth on
  the value of acceleration due to gravity at its
  equator.

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2. Effect of Coriolis Force

• Consider a point P at latitude ? on the surface
  of earth. Let the earth rotate with constant
  angular velocity ? about its polar axis.
• ? makes an angle ? with y- axis at point P

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• Imagine a point P vertically above P and drop a
  body of mass m, then velocity v acquired by it
  at time t is given by
• Vx and vy are taken as zero because body has
  velocity only along negative z-axis. The coriolis
  force acting on the particle is given by

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• This shows that coriolis force acts on the
  particle along positive x-axis.
• From Newtons second law of motion

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• Using the relation, v uat along negative
  z-direction.
• Integration w. r. t. time t gives

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• Again integrating w.r.t. t, we get
• Hence, due to coriolis force, the particle
  dropped vertically downwards suffers a deviation
  along positive x-axis i.e. towards east.
• The displacement of the particle will be maximum
  for ?0 i.e.
• at the equator.

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THANX!