# Does Centripetal Force Change Direction?

I have been struggling with this question that I have,

"Does centripetal force change direction?"

From every point, it points to the center. But if we draw its vector, we draw the tails from different point. How can we tell whether a vector has changed direction or not? Do we considered the vector's head too?

## 2 Answers

You have to consider the head in order to know what direction the vector is in, right? After all, that's half the point of having a head - to let you know what direction the vector points. (But keep in mind that, except for position or displacement vectors, the position at which you draw the head doesn't mean anything. The vector itself is located at the point where you draw its tail, and the head is just to show which direction it goes in and what its magnitude is.)

Now think about this: what direction is the centripetal force when the object is on the right side of its circle? What direction is the centripetal force when the object is on the top of its circle? Or on the left side? Are those all the same direction?

This is not really relevant to your question, but you have kind of stumbled on an issue that becomes very important in more complicated kinds of physics (specifically, general relativity): if you are comparing vectors at different points in space, how do you know what constitutes the "same direction" at different points? In a curved space, you can't assume that "left" at one point is the same as "left" at another point, for example. There is some fairly complicated math involved in determining how to "translate" a direction from one point to another. But in this case, you're not working in a curved space so you don't have to worry about any of that.

• so "does Fc change direction" – Raman CHAWRESH Sep 26 '14 at 5:38

A vector doesn't have a head and a tail. A vector in this context is something with a magnitude, and except for the zero vector, a direction. Another way to look at it: The displacement vector from the origin to the point with coordinates (1,1,1) and the displacement vector from the point with coordinates (2,2,2) to the point with coordinates(3,3,3) are the the same vector.

The angle between non-zero two vectors in three dimensional Euclidean space is determined by the ratio of the inner product between the vectors and the product of their magnitudes: $\cos\theta = (\mathbf a \cdot \mathbf b)/(||\mathbf a||\,||\mathbf b||)$. Once again, the head and tail don't come into play.

Does the centrifugal force change direction on an object moving along a circular path?
Imagine a kid on a playground roundabout. One moment the centrifugal force needed to keep her on the roundabout points south. A bit later, as the roundabout has made a quarter turn, the centrifugal force is pointing east. It's pointing north after yet another quarter of a turn, then west, then south again.

All that matters is the direction in which the force vector is pointing. If this direction changes over time, it's changing direction. It's as simple as that. You are overcomplicating things by asking about the head and tail of the vector.

• i am still at high school and you i don't understand anything from you answer. but can you answer my main question "Does Fc change direction" on a point that moves on a perfect circular path? – Raman CHAWRESH Sep 26 '14 at 5:37