04-17-08 - Circular Motion


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04-17-08 - Circular Motion

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