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04-17-08 - Circular Motion
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04-17-08 - Circular Motion

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Transcript

  • 1. Uniform Circular Motion
  • 2. What is uniform circular motion?
    • Movement of an object at constant speed around a circle with a fixed radius
    • Can the velocity be accelerated even though it has constant speed?
    • Yes, because the velocity may change due to direction. If direction changes and velocity changes then an object can accelerate.
  • 3. Describing Circular Motion
    • A lower case r represents the position of a vector
    • the direction of the vector can change but not its length (length is proportional to magnitude)
    • the acceleration of an object in uniform circular motion is always toward the center of the circle, called centripetal acceleration
  • 4. Equations
    • a c = v 2 /r
    • One complete revolution around a circle is called a period
      • Symbol is T
      • Units are seconds
    • an object will travel the distance of the circumference of the circle, which is represented by C = 2πr
    • v = 2πr/T
  • 5. Combining Equations
    • If we substitute the previous formula for v in the original formula for centripetal acceleration we would get
    • a c = 4π 2 r/T 2
    • Sometimes the force that causes centripetal acceleration is called centripetal force
    • Which direction is the net force?
    • The same direction as the acceleration
  • 6.
    • F net = ma c
    • F net = mv 2 /r
    • F net = m(4π 2 r/T 2 )
    • If you stop the acceleration, what direction will the object move?
    • The movement of the object is in the direction the velocity or tangent to the circle.