Question 99: Work, Energy and Power & Circular Motion

Question

For a particle in uniform circular motion, the acceleration $$\overrightarrow a $$ at any point P(R, $$	heta$$) on the circular path of radius R is (when $$	heta$$ is measured from the positive x-axis and v is uniform speed) :

Accepted Answer

As the particle in uniform circular motion experiences only centripetal acceleration of magnitude $$\omega$$
2
R or $${{{v^2}} \over R}$$ directed towards centre so from diagram,
$$\overrightarrow a  = {{{v^2}} \over R}\cos 	heta ( - \widehat i) + {{{v^2}} \over R}\sin ( - \widehat j)$$

Answer

$$ - {{{v^2}} \over R}\sin 	heta \widehat i + {{{v^2}} \over R}\cos 	heta \widehat j$$

Answer

$$ - {{{v^2}} \over R}\cos 	heta \widehat i + {{{v^2}} \over R}\sin 	heta \widehat j$$

Answer

$$ - {{{v^2}} \over R}\cos 	heta \widehat i - {{{v^2}} \over R}\sin 	heta \widehat j$$

Answer

$$ - {{{v^2}} \over R}\widehat i + {{{v^2}} \over R}\widehat j$$

Work, Energy and Power & Circular Motion

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) :

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