# [Physics] Why is the centripetal net force always to the center

centripetal-forcenewtonian-mechanicsreference framesvectors

I recently came across this diagram in my physics textbook

I got a bit confused by this diagram. I thought that the reason why the object accelerates towards the center is because of a net force, not because of velocities being added together.

So my question is: what forces do we use to determine that the centripetal force goes towards the center? I thought that we would use forces, and not velocities. Could you point out where I am confused?

$$\bullet$$ Note that the direction of the change in the velocity $$\Delta\textbf{v}$$ is towards the center. Therefore, the acceleration must be towards the center and hence also the force. Your diagram conveys the point that if a circular motion is uniform i.e., the magnitude of velocity remains fixed while its direction changes, the motion must be due to a force solely directed towards the center.
$$\bullet$$ The centripetal force may be provided by different agent in different situations. For the motion of planets around the sun, the centripetal force is provided by the gravitational attraction of the sun, for a stone tied to a string rotated in a circle the centripetal force is provided by the tension in the string and so on.