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Calculating the velocity given the position of the particle

  1. Aug 23, 2016 #1
    1. The problem statement, all variables and given/known data
    A particle moves with constant velocity along the curve r = e^(θ) and z = r (cylindrical coordinates). The speed, v, is constant.

    a) Calculate the velocity and acceleration of the particle in terms of θ and v.

    b) Show that the velocity and acceleration are perpendicular.

    c) Find the expression for θ(t).

    2. Relevant equations
    v
    = dr/dt (radial direction) + r dθ/dt (tangential direction)

    v^2 = (dr/dt)^2 + r^2 (dθ/dt)^2 = constant

    dr/dt = dr/dθ dθ/dt

    3. The attempt at a solution

    Mecaacutenica%20Teoacuterica_zpsvo48slj3.png
     
  2. jcsd
  3. Aug 23, 2016 #2

    haruspex

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    That's for 2 dimensions. This is moving in three.

    Posting your algebra as an image makes it hard to refer to specific equations in comments.

    Expressing dr/dt in terms of dθ/dt, then expressing that in terms of dr/dt is going round in circles. Get all the velocity components expressed in terms of the time derivative of one of the coordinates - r, θ, or z, whichever is easiest - as you eventually did.
     
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