What is centripetal acceleration?

[raydred]

I'm having trouble grasping the concept of centripetal acceleration on circular motion.
I understand angular velocity. From there what my books gives me is the centripetal accel formula. ac=(v^2)/R
I don't notice any acceleration in a circular motion. Nothing's accelerating.
What velocity is changing? In what direction? How would I calculate the position of an object by it's centripetal acceleration if:

• The object has "f" angular velocity.
• It is at "h" distance from the object it is orbiting.
• The object it is orbiting around has m mass.

Extra

Spoiler

The first thing I thought was that the centripetal acceleration was the acceleration of the angular velocity. So in a circular motion it would have to be ac=0 or it would disrupt the circle.
But I can't make ac=0 without having either v=0 or R=0. If this was true then the centripetal accel wouldn't be compatible with circular motion.
Then I kept reading in the internet, including in this site, that some regarded it as imaginary. Then I guess thought that maybe it was used to simplify some calculations related to centripetal force for circular motion but it's still blurry in my mind.

Continuing my spoiler's line of though, then again what's the difference between gravitational force and centripetal force?

Edit:I hope this is the right section. I hope I haven't forgot to say something. I hope someone can answer. Thank you.

 

[mathman]

I don't notice any acceleration in a circular motion. Nothing's accelerating.
What velocity is changing? In what direction?

According to Newton's first law, the object would continue in a straight line if there was no acceleration. The velocity change is that which keeps it in a circular path.

 

[raydred]

According to Newton's first law, the object would continue in a straight line if there was no acceleration. The velocity change is that which keeps it in a circular path.

Yes that is true. My thoughts are still blurry as I said so I have trouble asking questions about something which I don't even know what it is.
I understand there has to be an acceleration to keep it a circular orbit. But I'm still confused about the rest of my questions.
Then the gravitational accel would be the same as the centripetal accel?... I think I'm repeating myself but I thought I should reply.

 

[Doc Al]

I don't notice any acceleration in a circular motion. Nothing's accelerating.

Acceleration means a change in velocity. Since velocity is a vector, that could mean something speeding up, slowing down, or changing direction. In uniform circular motion, the velocity is constantly changing direction towards the center.

 

[Doc Al]

Continuing my spoiler's line of though, then again what's the difference between gravitational force and centripetal force?

"Centripetal force" is just the name given to the net inward force that must exist in circular motion. To have circular motion, something must provide a centripetal force. In the case of a satellite orbiting a planet (say), the gravitational force provides the centripetal force.

 

[raydred]

changing direction

But it must be gradually... yes?
But this and packed with a friend's explanation made me understand the concept I think. Thank you two.