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I know for a fact that if a particle is moving in a circle such that the value of radial acceleration is non-zero and the value of tangential acceleration is zero ,then it can be classified as circular motion.But I was wondering if the opposite can be true ,i.e. $a_t\neq 0$ and $a_r= 0$ ? Would the particle be moving in a circle if this was to happen?

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To directly answer your question, assuming the particle is somehow confined to a circular motion then either the speed is 0 or the radius is infinite (i.e. a straight line), since $0 = a_r = \frac{v^2}{r}$.

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    $\begingroup$ So if I have a spinning wheel, and I want to change its direction by applying a constant torque, then exactly at the moment the angular velocity is changing sign it is zero, there is no speed and hence no centripetal acceleration, but there is tangential acceleration. They only catch is a particle on the wheel is not moving at this point, so maybe you can't really say it is moving in a circle. $\endgroup$ Oct 13 '15 at 20:03

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