Pytels Dynamics 12.14: particle moves on helix

[Alexanddros81]

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 v_z = dz/dhxdh/dt
what dh/dt is equal to? Since h = 0.75m = constant, then v_z=0 and a_z = 0
Is my asumption correct?

 

[scottdave]

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.

 

[Alexanddros81]

Can you chek my solution?
My results are the same as Pytels

 

[scottdave]

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 canceled out the pi, so that v_z = -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.