For circular motion,if vec a_t,vec a_c,vec r | vedclass

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(C) In circular motion,the tangential acceleration $\vec a_t$ is directed along the tangent to the path,and the centripetal acceleration $\vec a_c$ is

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$\vec a_c \cdot \vec v$ may be positive or negative

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(C) In circular motion,the tangential acceleration $\vec a_t$ is directed along the tangent to the path,and the centripetal acceleration $\vec a_c$ is directed towards the center of the circle along the radius.Since the tangent is perpendicular to the radius,$\vec a_t$ and $\vec a_c$ are perpendicular to each other. Therefore,$\vec a_t \cdot \vec a_c = 0$.The velocity vector $\vec v$ is always directed along the tangent to the path. Since $\vec a_c$ is directed towards the center (along the radius),$\vec a_c$ is always perpendicular to $\vec v$. Therefore,$\vec a_c \cdot \vec v = 0$.The tangential acceleration $\vec a_t$ is parallel or anti-parallel to the velocity vector $\vec v$. If the speed is increasing,$\vec a_t$ and $\vec v$ are in the same direction,so $\vec a_t \cdot \vec v > 0$. If the speed is decreasing,$\vec a_t$ and $\vec v$ are in opposite directions,so $\vec a_t \cdot \vec v Comparing these with the given options,the statement $\vec a_c \cdot \vec v$ may be positive or negative is incorrect because $\vec a_c \cdot \vec v$ is always zero.

For circular motion,if $\vec a_t$,$\vec a_c$,$\vec r$ and $\vec v$ are tangential acceleration,centripetal acceleration,radius vector and velocity respectively,then find the wrong relation.

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