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I have a big confusion. There is a question in my book which basically says that a ball is tied to a string and rotated. and it asks me to tell whether the following statement is true of false. Direction of radial acceleration MAY remain the same. This statement is true. Please explain to me a case where this is possible. i thought that this is only when an object moves straight and in circular motion radial acceleration is towards the centre.

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    $\begingroup$ I think you'd better tell us exactly how this is worded, instead of "basically says". The exact wording may make all the difference. Also, your last sentence needs editing. I don't understand it at all. Certainly, if a ball is tied to a string and rotated, the direction of acceleration does not remain the same. $\endgroup$ – garyp Sep 13 '14 at 21:26
  • $\begingroup$ The direction will vary continuously in a Cartesian coordinate system, but it will always point in the $\hat{e}_r$ direction in a polar coordinate system. Thus, technically the acceleration could "point in the same direction" in a polar coordinate system, but not in a Cartesian one. Of course, the radial direction itself is rotating around the origin all the while. $\endgroup$ – Bryson S. Sep 13 '14 at 23:06
  • $\begingroup$ @garyp this is the exact question. if you cant answer it don't blame the question! $\endgroup$ – Jai Mahajan Sep 14 '14 at 6:05
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    $\begingroup$ Watch your manners. Your posting has at least one error, so I do blame the question. "Direction of radial acceleration MAY remain the same" is false, but your post says that it is true. $\endgroup$ – garyp Sep 14 '14 at 12:09
  • $\begingroup$ @garyp the statement is true! $\endgroup$ – Jai Mahajan Sep 14 '14 at 12:28
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There exists no case where radial acceleration does not change direction.

But i thought of a quite eccentric stuff like this where it appears that it does not change direction.Suppose as the ball tied to the string revolves,there is an observer who is moving along with the string facing the ball.Then, in that frame of reference the direction does not change.

Note:The observer must not be placed on the ball-then relative acceleration becomes 0.

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  • $\begingroup$ As you say, in the rotating frame there is no acceleration, so the acceleration has no direction! There is nothing to "remain the same". The statement is also "true" if the speed and radius of the ball are both zero. I think that the statement is false, and the question is very poor. I wonder what book it comes from? $\endgroup$ – garyp Sep 14 '14 at 13:11
  • $\begingroup$ there is no acceleration relative to the motion of the ball $\endgroup$ – Jai Mahajan Sep 14 '14 at 13:18
  • $\begingroup$ this statement is correct for sure. $\endgroup$ – Jai Mahajan Sep 14 '14 at 13:21
  • $\begingroup$ Well, we can take the limit as radius grows without bound while velocity remains finite, causing $\frac{\mathrm{d}\vec{r}}{\mathrm{d}t}$ to approach zero, but of course that is a monumentally uninteresting case. $\endgroup$ – dmckee Sep 14 '14 at 17:35

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