Intuitive understanding of centripetal vs. centrifugal force I am having trouble understanding how centripetal force works intuitively.
This is my claim.
When I have a mass strapped on a string and spin it around, I feel the mass pulling my hand.
So, I want to say that the mass is trying to move away from the center of the circle, and yet centripetal force makes it move in a circle, i.e, centripetal acceleration towards the center.
Similarly, when I am driving a car and making a curve, I feel being pushed away from the center of the curvature rather than towards it.
I am having so much trouble with these types of problems because of this counter intuitive concept. 
Can someone help me out?
 A: The centripetal force is the one which mantains an object in a circular motion (changing the direction of velocity).

when I am driving a car
  and making a curve, I feel being
  pushed away from the center of the
  curvature rather than towards it.

In this case you are feeling inertia, your body tries to continue in straight motion. However, from you accellerated frame you can describe inertia as a centrifugal force.
So the problem is that you are confusing centripetal and centrifugal force. The former pushes you to the center, while the latter is a virtual force which pushes you to the outside.
A: Here's another way to approach the issue you're having. Forget about circular motion and consider linear acceleration. When you're sitting in a car on a straight road, and then it speeds up, you accelerate forward. That is, there's a net force on you in the forward direction. However, in the car you feel like you're being push back into your seat; if the seat weren't there, your motion relative to the car would be backward.
This is exactly what's going on in the circular case while moving at constant speed; there's a net force on you toward the center of the circle, but it feels you're being pushed away from the center of the circle. Only we give them fancy names like centripetal and centrifugal.
For more info, look up terms like virtual force, pseudo force, or non-inertial frame.
