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Displacement and arc length problems

  1. Oct 17, 2012 #1
    1. v=s/t where s represents the displacement
    2. s=rθ where s represents the arc length

    v=rθ /t

    Why can substitute here?
    I guess that is not same things.

    An arc length is not a straight line but displacement is which is shortest distance between initial and final point.
     
  2. jcsd
  3. Oct 17, 2012 #2

    Philip Wood

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    Not quite sure I've grasped your difficulty, but for the reasoning to be valid, s in equation (1) must represent not a displacement but the arc length s. Thus v is not mean velocity over s, but speed.
     
  4. Oct 18, 2012 #3
    Thanks. I understand now.
    The equation of (1) is not velocity=displacement/time, but speed=distance/time, right?
     
  5. Oct 18, 2012 #4

    Philip Wood

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  6. Oct 19, 2012 #5
    But I have some problems about it.
    v=rθ /t

    θ /t = angular velocity
    Why speed = radius x angular velocity?
    I think velocity = radius x angular velocity is suitable for it.
     
  7. Oct 19, 2012 #6

    Philip Wood

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    I assume you are not treating radius and angular velocity as vectors. If you're treating them as scalars, as in most introductory courses, then the multiplication yields a scalar, which is better called speed than velocity.

    In more advanced work it is possible to assign a direction to angular velocity (making it a pseudo vector), and it is clearly possible to treat instantaneous radius as a vector. By assigning a special meaning to multiplication we can produce the instantaneous velocity vector.
     
  8. Dec 14, 2012 #7
    what is the weight of a ship that displaces 500,000 kg of water?
     
  9. Dec 14, 2012 #8

    SteamKing

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    500 tonnes, more or less.
     
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