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.