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Circular motion

  1. Jan 8, 2015 #1
    Good afternoon!
    Exercise: Prove that if a body moves under the action of a force F = k⋅u × v, where u is an arbitrary unit vector and v the velocity, the motion is circular with angular velocity ω = k ⋅ u or, in a more general case, a spiral parallel to u.

    Source: (Alonso & Finn: Fundamental university physics)

    I attempted to prove that F is a central force, so that the angular momentum is constant. Is that wrong?
    Thank you in advance!
     
  2. jcsd
  3. Jan 8, 2015 #2

    vela

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    Would showing F is a central force buy you anything? The force of the Sun on a planet is a central force. but the orbits aren't circular.
     
  4. Jan 8, 2015 #3

    haruspex

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    That won't do it. F = k.v would satisfy that. Get an equation for the acceleration.
     
  5. Jan 9, 2015 #4
    Thank you for your responses! In order to prove that it's motion is circular wouldn't it be sufficient to prove that ω is constant?
    Could you "boost" me a bit?
     
  6. Jan 9, 2015 #5

    haruspex

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    Not really. The question is asking you to demonstrate that the equation of motion corresponds to a particle moving at constant speed in a helix. (It says spiral, but it means helix.)
    It might help if you could write down the general equation for such a motion, so that you could see what the answer has to look like. Hint: pick a suitable set of orthogonal unit vectors.
    Anyway, the first (easy) step, as I posted originally, is to obtain an equation for the acceleration of the particle.
     
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