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- Homework Statement
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- Relevant Equations
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I am trying to derive the tangential acceleration of a particle. We have tangential velocity, radius and angular velocity. $$v_{tangential}= \omega r$$ then by multiplication rule, $$\dot v_{tangential} = a_{tangential} = \dot \omega r + \omega \dot r$$ and $$a_{tangential} = \ddot \theta r + \dot \theta \dot r$$ However, we also have $$\vec{a} = (\ddot r - r \dot \theta^2)\hat{r} + (r \ddot \theta + 2 \dot r \dot \theta)\hat{\theta}$$, which implies $$a_{tangential} = \ddot \theta r + 2 \dot \theta \dot r$$

Now, what's wrong?

Now, what's wrong?