For a particle in uniform circular motion, the acceleration an at $straight a with rightwards arrow on top$ point P (R, θ) on the circle of radius R is (Here θ is measured from the x–axis)

$negative straight v over straight R space cos space straight theta space bold i with bold hat on top space plus space straight v squared over straight R space sin space straight theta space bold j with bold hat on top$
$negative straight v over straight R space sin space straight theta space bold i with bold hat on top space plus space straight v squared over straight R space cos space straight theta space bold j with bold hat on top$
$negative straight v over straight R space cos space straight theta space bold i with bold hat on top space minus space straight v squared over straight R space sin space straight theta space bold j with bold hat on top$
$straight v squared over straight R space straight i with hat on top space plus fraction numerator begin display style straight v squared end style over denominator begin display style straight R end style end fraction space straight j with hat on top$

Solution

negative straight v over straight R space cos space straight theta space bold i with bold hat on top space minus space straight v squared over straight R space sin space straight theta space bold j with bold hat on top

straight a with rightwards arrow on top space equals space minus space straight V squared over straight R space cos space straight theta space straight i with hat on top space minus space straight V squared over straight R space sin space straight theta space straight j with hat on top

Some More Questions From Laws of Motion Chapter

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