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For a particle in uniform circular motion the acceleration \( \vec{a} \) at a point \( P(R, \theta) \) on the circle of radius \( R \) is (here \( \theta \) is measured from the \( x \)-axis).
(1) \( -\frac{v^{2}}{R} \cos \theta \hat{i}+\frac{v^{2}}{R} \sin \theta \hat{j} \)
(2) \( -\frac{v^{2}}{R} \sin \theta \hat{i}+\frac{v^{2}}{R} \cos \theta \hat{j} \)
(3) \( -\frac{v^{2}}{R} \cos \theta \hat{i}-\frac{v^{2}}{R} \sin \theta \hat{j} \)
(4) \( \frac{v^{2}}{R} \hat{i}+\frac{v^{2}}{R} \hat{j} \)
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