Pytels Dynamics 12.14: particle moves on helix

  • #1

Homework Statement


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

Homework Equations




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?
 

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Answers and Replies

  • #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.
 
  • #3
Can you chek my solution?
My results are the same as Pytels
 

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  • #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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