This question already has an answer here:

I know that the force is used to change the direction of the velocity but my question is while it has 3 options either to pull the object towards the center or change the direction of velocity or both. It would have been more appropriate if it did both.


marked as duplicate by stafusa, Cosmas Zachos, Kyle Kanos, David Z Oct 5 '17 at 2:37

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Possibly related: physics.stackexchange.com/q/9049/2451 $\endgroup$ – Qmechanic Oct 4 '17 at 18:12
  • $\begingroup$ What do you mean? It is impossible for a massive object to follow a circular path at a constant speed unless some force acts on the object, pushing it (or pulling it, both mean the same thing in this case) toward the center of the circle. $\endgroup$ – Solomon Slow Oct 4 '17 at 18:12
  • $\begingroup$ Simply put, an object in circular motion is being pulled towards the center of the circular path; pulled isn't synonymous with move, i.e., an object needn't move towards the center in order to be pulled towards it. $\endgroup$ – Alfred Centauri Oct 5 '17 at 2:31

The radial acceleration due to centripetal force is just enough to make the object miss the center by the same amount every instant, which results in the distance to the center remaining constant. This is why the motion is circular in the first place; if the acceleration was bigger, the particle would indeed spiral inwards. Smaller acceleration and it would spiral outwards. At a certain inward acceleration equal to radius times angular velocity squared, the particles orbit is circular.

Instead of starting with an acceleration towards the center, and asking what the motion looks like, start with the motion, and ask what the acceleration must be.

With no acceleration, the object would travel in a straight line, eventually winding up quite far away from the "center" point. Pay careful attention to what that means: with no radial acceleration, the radius gets bigger! This has to do with one of the tricky features of talking about "the radial direction" at all: the direction meant by "radial" keeps changing as you move, but the actual motion doesn't change direction without outside interference. This means that you can go from zero "radial velocity" to nonzero "radial velocity", without your velocity actually changing at all! This means you have to be careful, and you can't think about radial distance the same way you think about things like x, y, or z position (at least, not without adding in some other factors and being careful about it).

No acceleration means an increasing distance from the center. So, if we want it to stay a constant distance from the center instead (which is required for circular motion), there must be acceleration towards the center. If you do out the geometry, you find that the required acceleration is the one given in the textbooks: $$ a = \frac {v^2}{r} $$

With radial acceleration more than this, the body would actually fall to the centre.

Also, you should consider velocity as a vector quantity. Newton's second law says that the external force changes the $\vec {velocity} $. Here, it changes the $\vec{velocity} $ by changing its direction and not magnitude.


As the centripetal force acts upon an object moving in a circle at constant speed, the force always acts inward as the velocity of the object is directed tangent to the circle. This would mean that the force is always directed perpendicular to the direction that the object is being displaced.


Not the answer you're looking for? Browse other questions tagged or ask your own question.