Why Does Centripetal Force Equal Friction in Circular Motion?

[HelloMotto]

ok the textbook says Centripetal Force always points towards the centre of circle as well as the Centripetal acceleration. But Why?

Also I was given a diagram in the textbook like the one below. I don't understand why
Fc = the friction force...
http://img258.imageshack.us/img258/430/diagram1lh3.png
http://g.imageshack.us/g.php?h=258&i=diagram1lh3.png

could you guys explain this to me please?

 

[Kurdt]

The force must always point toward the centre of a circle to keep the particle or object moving round in a circle. I don't know why the centripetal force equals the friction force, it depends on the context. Could you give more information?

 

[HelloMotto]

thank you.
that diagram i posted comes from a question related to car that is rounding a curve on a level road.

 

[Kurdt]

In that case the centripetal force will equal the static friction when the car is going round the curve at a speed just before slipping. If you go round a curve too fast the friction will not be enough to keep the car from sliding and you will skid off.