Why centripetal force does not pull the object towards the center? [duplicate]

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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

• Possibly related: physics.stackexchange.com/q/9049/2451 – Qmechanic Oct 4 '17 at 18:12
• 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. – Solomon Slow Oct 4 '17 at 18:12
• 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. – 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.

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: $$a = \frac {v^2}{r}$$
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.