- #1
ryan88
- 42
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Hi,
I have a couple of questions about velocities in inertial and rotating frames of reference, related by the following equation:
[tex]\mathbf{v_i} \ \stackrel{\mathrm{def}}{=}\ \frac{d\mathbf{r}}{dt} =
\left( \frac{d\mathbf{r}}{dt} \right)_{\mathrm{r}} +
\boldsymbol\Omega \times \mathbf{r} =
\mathbf{v}_{\mathrm{r}} + \boldsymbol\Omega \times \mathbf{r}[/tex]
Thanks,
Ryan
I have a couple of questions about velocities in inertial and rotating frames of reference, related by the following equation:
[tex]\mathbf{v_i} \ \stackrel{\mathrm{def}}{=}\ \frac{d\mathbf{r}}{dt} =
\left( \frac{d\mathbf{r}}{dt} \right)_{\mathrm{r}} +
\boldsymbol\Omega \times \mathbf{r} =
\mathbf{v}_{\mathrm{r}} + \boldsymbol\Omega \times \mathbf{r}[/tex]
- [itex]\mathbf{v_i}[/itex] and [itex]\mathbf{v_r}[/itex] both state which frame of reference they are measured in, however [itex]\mathbf{r}[/itex] does not. Is this supposed to be in the inertial or rotating frame of reference?
- If I use the equation to find the velocity in the rotating frame, does this mean that the value is represented in the rotating frame of reference? Or is it that the magnitude of that velocity is correct, but it still needs to be rotated to the rotating frame of reference?
Thanks,
Ryan