Position vector in spherical coordinates.

[vwishndaetr]

I have not done this in a while and I am having a brain fart.

Given: A wheel of radius R rotates with angular velocity Ct² k\hat{} (lies in x-y plane, rotating about z). A point P on the circles is P(x,y,z) = (0,R,0)

Ques: What is the position vector of point P in spherical coordinates?

Ans: Now I know that P(x,y,z) -> P(r,\theta,\phi,) = (R, \pi/2,\pi/2)

I want to say P(r,\theta,\phi,) = R \hat{r} + \{pi/2}\hat{\theta} + \{pi/2}\hat{\phi}, but that tells me P never moves. Considering P is on a spinning disk, it must some how correlate to Ct² \hat{k}


Maybe I'm just overlooking this. Can some one point me in the right direction?

 

[vwishndaetr]

sorry, having coding issues.

 

[vwishndaetr]

any ideas

 

[vwishndaetr]

I cleaned up the presentation a bit, hopefully to make it a bit easier for those that can share some advice.

Given: A wheel of radius R rotates with an angular velocity. The wheel lies in the xy plane, rotating about the z-axis.

P(x,y,z) = (0,R,0)

\overrightarrow{\omega}= Ct^2\hat{k}

Ques: What is the position vector of point P in spherical coordinates?

Ans: Now I know that,

P(r,\theta,\phi,) = (R,\frac{\pi}{2},\frac{\pi}{2})

But I don't think that helps much.

For the position vector, I can't figure out the term for:

\hat{\phi}

I have:

\overrightarrow{r}= R\ \hat{r}+\frac{\pi}{2}\ \hat{\theta}+\ \ \ \ \ \ \ \ \hat{\phi}

The last term is giving me issues.

 

[vwishndaetr]

Now I know that \phi changes with time, so the term must depends on t.

I also know that \omega is rad/s, which can also be interpreted as \phi/s.

But I don't think it is legal to just integrate \omega to get position. Is it?

Since the angular velocity is quadratic, that means the disc is accelerating. So the position should be third order correct?

I'm being really stubborn here because I know it is something minute that is keeping me from progressing.