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Pytels Dynamics 12.14: particle moves on helix

  1. Jun 17, 2017 #1
    1. The problem statement, all variables and given/known data
    When a particle moves along the helix shown, the componentsof its position vector are
    x=Rcosωt , y = Rsinωt , ##z=-\frac h {2π} ωt##

    where ω is constant. Show that the velocity and acceleration have constant magnitutes,
    and compute their values if R=1.2m, h=0.75m, and ω=4π rad/s
    2. Relevant equations


    3. The attempt at a solution
    for a start I would like someone to tell me by computing vz = dz/dhxdh/dt
    what dh/dt is equal to? Since h = 0.75m = constant, then vz=0 and az = 0
    Is my asumption correct?
     

    Attached Files:

  2. jcsd
  3. Jun 17, 2017 #2

    scottdave

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    You would not take a derivative with respect to h : h and R are parameters which someone would choose to describe a specific shape and size of helix. Imagine a tightly wound screw, then you have h (the gap between adjacent helix "threads") small in relation to R. If h is larger then it will be a "shallower" spiral (imagine a drill bit). so h and R are considered constants, in this case.
     
  4. Jun 18, 2017 #3
    Can you chek my solution?
    My results are the same as Pytels
     

    Attached Files:

  5. Jun 18, 2017 #4

    scottdave

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    It looks right to me. I didn't get out the calculator and check all the numbers. They appear to be in the ballpark, though.

    One thing: I would keep the units when doing the work. You made the substitution of w = 4pi and then cancelled out the pi, so that vz = -2h ; which when first looking at it, looks like a distance, not a velocity. But the w carried a dimension of (1/time), which would restore the [Length]/[Time] dimensions of velocity. (radian angle measure is considered dimensionless in most cases.
     
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