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Homework Statement
An ant walks from the inside to the outside of a rotating turntable. Write down it's velocity vector.
Use polar the cartesian coordinates.
Homework Equations
I have already derived the velocity vector in polar coordinates which is:
[tex]\hat{v}[/tex] = [tex]\dot{r}[/tex][tex]\hat{r}[/tex] + r[tex]\dot{\vartheta}[/tex][tex]\hat{\vartheta}[/tex]
The Attempt at a Solution
The table is rotating at a velocity [tex]\hat{v}[/tex] whilst the ant we assume just walks in a straight line along direction[tex]\hat{j}[/tex] in it's reference frame there is nothing odd, it is walking in a straight line. However in the observers reference frame is is moving in a circle due to the motion of the turntable.. So do I take it's cartesian velocity vector [tex]\dot{r}[/tex][tex]\hat{r}[/tex] and simply add it with the velocity of the turntable [tex]\dot{r}[/tex][tex]\hat{r}[/tex] + r[tex]\dot{\vartheta}[/tex][tex]\hat{\vartheta}[/tex] ??
I'm not quite sure how this works.