# Acceleration on a helix

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1. Apr 25, 2015

### sitzpillow

Dear physicist,
my task is to calculate the acceleration of a particle of mass m which moves without friction in the earth's gravitational field on a helix:
The helix is parameterized as shown:

$$x(\phi)=a cos \phi$$
$$y(\phi)=a sin \phi$$
$$z(\phi)=c \phi$$

formed with a radius a,gradient c as constants and the angle $$\phi$$ which mimics the projection of the radius vector on the x, y plane of the axis x with $$\phi \in 0<= \phi<\infty$$

What is the relationship between the arc length s and the angle phi?
Also, I need to derivate the tangents, normals and binormal vector by using $$\overrightarrow{r}(s)$$
and calculate the end nor the path velocity (with s (t = 0) = 0, s' (0) = 0).

I'm afraid not to have any approaches to solve the problem :/
I would appreciate every hint.

2. Apr 25, 2015

### PeroK

Can you think of a conserved quantity that might make this problem easier?

You may also want to consider velocity expressed in other than Cartesian coordinates (if that isn't giving too much help!).

3. Apr 25, 2015

### Staff: Mentor

@sitzpillow -- You are required to show us your efforts toward the solution before we can offer much tutorial help. Please use the hint provided by PeroK and show us your efforts...