Why Does Centripetal Force Equal Friction in Circular Motion?

AI Thread Summary
Centripetal force is essential for maintaining circular motion, always directed towards the center of the circle. In the context of a car rounding a curve, the centripetal force equals the static friction force at the threshold before slipping occurs. If the car exceeds a certain speed, the friction is insufficient to provide the necessary centripetal force, leading to skidding. Understanding this relationship is crucial for analyzing motion in circular paths. The discussion emphasizes the importance of friction in enabling safe navigation around curves.
HelloMotto
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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?
 
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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?
 
thank you.
that diagram i posted comes from a question related to car that is rounding a curve on a level road.
 
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.
 

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