For a particle in uniform circular motion, the acceleration \( \vec{a} \) at any point \( P(R, \theta) \) on the circular path of radius \( R \) is (when \( \theta \) is measured from the positive \( x \)-axis and \( v \) is uniform speed) :
\( -\frac{v^2}{R}\sin\theta\,\hat{i} + \frac{v^2}{R}\cos\theta\,\hat{j} \)
\( -\frac{v^2}{R}\cos\theta\,\hat{i} + \frac{v^2}{R}\sin\theta\,\hat{j} \)
\(- \frac{v^2}{R}\cos\theta\,\hat{i} - \frac{v^2}{R}\sin\theta\,\hat{j} \)
\( -\frac{v^2}{R}\,\hat{i} + \frac{v^2}{R}\,\hat{j} \)
