Centripetal acceleration?

It seems that centripetal acceleration should be in the same direction as the velocity vector.
Why is it directed into the center of the circle. I remember walter lewin talking about a marble inside a glass test tube. Imagine the marble inside of it and I swing the test tube like a baseball bat horizontal to the ground. When i first start to swing the bat i push the marble with the side of the test tube and the marble wants to go in a straight line, and the reason it goes out towards the end is because when i move the test tube, I have allowed the marble moving in a straight line to occupy the end of the test tube. So why is the acceleration into the center of the circle.

Doc Al
Mentor
It seems that centripetal acceleration should be in the same direction as the velocity vector.
Once the marble has reached the end of the tube and is executing uniform circular motion, what is its acceleration? Compare how the velocity vector changes from moment to moment and you'll see why the acceleration is centripetal.

ok i see thanks for your response .

tiny-tim
Homework Helper
When i first start to swing the bat i push the marble with the side of the test tube and the marble wants to go in a straight line, and the reason it goes out towards the end is because when i move the test tube, I have allowed the marble moving in a straight line to occupy the end of the test tube. So why is the acceleration into the center of the circle.

hi cragar! no, before the marble reaches the end, the only force is tangential (from the side of the tube), so the acceleration is purely tangential

the radial acceleration is r'' - v2/r, and that has to be zero!

the radial acceleration doesn't become non-zero until there's a force from the end of the tube (forcing r'' = 0, of course) so is the radial acceleration produced because the marble wants to move in a straight line but the end of the tube is pushing on it?

tiny-tim
Homework Helper
so is the radial acceleration produced because the marble wants to move in a straight line but the end of the tube is pushing on it?

acceleration can only be produced by a force …

the only force is from the glass of the tube …

initially it's tangential, but yes when the marble gets to the end it's radial (and forget about where "the marble wants to move" … that's its present velocity, whcih has nothing to do with acceleration)