For a particle in uniform circular motion, acceleration overrightarrow{ a } at any point P ( R , θ)

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3-2.Motion in Plane

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For a particle in uniform circular motion, the acceleration $\overrightarrow{ a }$ 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)

A

$-\frac{v^{2}}{R} \sin \theta \hat{i}+\frac{v^{2}}{R} \cos \theta \hat{j}$

B

$-\frac{v^{2}}{R} \cos \theta \hat{i}+\frac{v^{2}}{R} \sin \theta \hat{j}$

C

$-\frac{v^{2}}{R} \cos \theta \hat{i}-\frac{v^{2}}{R} \sin \theta \hat{j}$

D

$-\frac{v^{2}}{R} \hat{i}+\frac{v^{2}}{R} \hat{j}$

Solution

$a=|\vec{a}|=\frac{ V ^{2}}{ R }$

$\vec{a}=-a \cos \theta \hat{i}-a \sin \theta \hat{j}$

$=-\frac{V^{2}}{R} \cos \theta \hat{i}-\frac{V^{2}}{R} \sin \theta \hat{j}$

Standard 11

Physics

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