Centripetal acceleration - why?

[Cloud 9]

Just a general "why" question. Why does the centripetal acceleration increase when the radius decreases? This is not a homework question but rather something I'm trying to make sense of. I read that: "The centripetal acceleration has to continuously change the velocity vector back towards the center of the circle to keep the object moving in a circle."

So shouldn't it be that when the distance from the circle is higher (radius), the centripetal acceleration is higher to change the velocity vector back towards the center?? That isn't the case though since: as the radius decreases, the centripetal acceleration increases...why is this so?

 

[Feldoh]

Imagine a ball traveling in a circle at a constant speed.

If we change the radius of this ball the only difference is that the direction of the ball will change at a different rate. Also, remember that a change in direction is an acceleration. So a ball can be accelerating even at a constant speed IF it is changing direction.

It appeals to the mind that if the ball is on a shorter radius the direction will change faster (and hence) the acceleration will be larger than if the ball were really far away. This makes sense because the distance the ball has to travel to complete one full circle is a lot less if the radius is smaller.

 

[Cloud 9]

Thanks, that makes more sense. That sentence is just worded weirdly I guess. I'm terrible at physics anyway, give me a chemistry or organic chemistry equation and I'm all on it. lol...well thank you again, I appreciate the help!

 

[gomunkul51]

centripetal acceleration = tangential velocity squared / radius

are you familiar with that ?