Given a position function of a particle:
r = rr^(θ) ( $$ \mathbf r=r\,\hat{\mathbf r}\left(\theta\right), $$ where r^(θ)$\hat{\mathbf r}(θ)$ is the polar unit vector)
, to find the velocity, we take the derivative which results in:
v = dr/dt = (dr/dt) r^(θ) + r(dr^(θ)/dt).$$ \mathbf v = \frac{\mathrm d\mathbf r}{\mathrm dt} = \frac{\mathrm dr}{\mathrm dt} \hat{\mathbf r}(θ) + r\frac{\mathrm d\hat{\mathbf r}(θ)}{\mathrm dt}.$$
What does each term in the velocity equation mean?
