Centripetal Force and Radius

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Hi, I'm currently studying for a physics test tomorrow, but something that has been confusing me is centripetal force.

My textbook states that, "Traveling in a circular path with a smaller radius of curvature requires a greater centripetal force".

But my question is, why, and how is that true? I would have assumed at first that if the radius was getting shorter, then the centripetal force would be decreasing, and not increasing.

So why exactly, and how does having a shorter radius result in greater centripetal force?

Thanks :)
 

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