Physics 101: Lecture 11 Centripetal Force

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Physics 101 Lecture 11Centripetal Force

• Brief Review of Chapters 1-4
• Textbook Chapter 5
• Uniform circular motion
• satellites in circular orbits, apparent
  weightlessness and
• artificial gravity

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Centripetal Force
Centripetal acceleration
Acceleration is the result of a net-force acting
on an object. In case of ac this net-force is
called centripetal force, Fc Magnitude of Fc
Fc S F m ac m v2/R Direction of Fc always
points towards the center of
the circle
Define frequency f, period T, angular velocity w
The period T is the time required to travel once
around the circle, ie to make one complete
revolution T2p R/v
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Satellites in Circular Orbits

• Satellites in circular orbits are examples of
  uniform circular motion.
• What provides the centripetal force ?
• The gravitational pull of the earth Fc G M
  m/r2 mv2/r
• Orbital speed of statellite v (GM/r)1/2 gt
  v does not depend on mass of satellite !
• Synchronous satellites Orbital period T1 day
  time it takes for the earth to turn once around
  its axis.
• gt Satellite always appears to be at a fixed
  position in the sky -gt stationary relay stations
  for communication signals sent up from earth.

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Synchronous Satellites

• To serve as stationary relay station the
  satellite must be placed at a certain height
  above the earth surface
• T1 day8.64 x 104 s 2p r/v and
  v(G M/r)1/2
• r3/2T (GM)1/2/(2p) gt r4 x 107 m
• Hr-rE3.6 x 107 m 22300 miles

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Circular Motion More Examples

• Apparent weightlessness
• Apparent weight in a satellite is zero just as
  in a free
• falling elevator
• Person and scale fall with the same
  acceleration towards the center of earth gt they
  cannot push against each other.
• Artificial Gravity In a rotating space
  laboratory a push on
• A persons feet equal to mg can be simulated by
  the
• centripetal force if v (r g)1/2.