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## Homework Statement

Calculate the work [tex]W_{A B}[/tex] done by the force [tex]F[/tex] using Newton's laws ([tex]F=ma[/tex], etc), when a particle moves from the point [tex]A[/tex] to the point [tex]B[/tex] along the unit circle. The angle is [tex]\theta[/tex]. No friction. How do you define kinetic energy in polar coordinates?

## Homework Equations

Acceleration in polar coordinates is:

[tex] \bar{a} = ( \ddot{r} - r ( \dot{ \theta } )^2 ) \hat{r} + ( r \ddot{ \theta } + 2 \dot{ r } \dot{ \theta } ) \hat{ e_{\theta} }[/tex]

## The Attempt at a Solution

I know from cartesian coordinates that [tex]PE=KE <=> 1/2 * mv^2 = mg*h [/tex]. I should verify it in polar coordinates. So integrating [tex]\bar{a}*m[/tex], with respect to the radius [tex]r[/tex] and the angle [tex] \theta[/tex], probably give me the energy, like [tex] W=F*distance [/tex] in carteesian coordinates.

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