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How can acceleration be perpendicular to velocity at any given time?

  1. Sep 28, 2010 #1
    How can acceleration be perpendicular to velocity at any given time?
    Is it because when ther is a circular path, there can be lines drawn tanget to the circular path that it follows? I don't understand!
  2. jcsd
  3. Sep 28, 2010 #2
    If you suddenly release an object rotating around a circle, which direction does it go?
  4. Sep 28, 2010 #3
    When you make an object twirl on the end of a string, you're always pulling aren't you?

    To pull something is to cause acceleration! (unless the object pulled on is fixed)
  5. Sep 29, 2010 #4
    The direction of the velocity at any point is tangential to the circle at that point.To find the change of velocity between two points you can perform a vector subtraction of the velocities at the two points and to find the average acceleration between the points divide the velocity change by the time.To find the instantaneous acceleration consider the limit where the angular separation between the points approaches zero.You will find that the direction of the acceleration is towards the centre of the circle.
  6. Sep 29, 2010 #5
    This is because the velocity at a particular instant is directed along tangent at that point while the acceleration is always directed towards the center of the circle. Clearly these two are perpendicular to each other.
  7. Sep 30, 2010 #6
    Remember that velocity is a vector quantity and acceleration is the time rate of change of velocity. Since velocity is a vector it has both direction and magnitude; therefore a change in velocity can be a change in magnitude (speed) or a change in direction.

    You can break any acceleration vector into components along the line of velocity and perpendicular to the velocity. The component of acceleration along the direction of velocity changes the speed, and the perpendicular component changes the direction.
  8. Sep 30, 2010 #7


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    I could put it yet another way:
    Acceleration is rate of change of velocity. Velocity is speed and direction. If the speed is constant (it's just going round and round), it is only the direction that is changing for a circular path. The change of direction is along a radius so that is the direction where the acceleration is.
    Also, if the string is totally flexible, then it can ONLY pull along a radius. That means that the only possible direction of acceleration must be along a radius as it's the only direction that any force is acting.
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