If you have ever been down a water-slide (a flume) you will know that you tend to slide up the side as you go around a bend. Explain how this provides the centripetal force needed to push you around the bend. Explain why you slide higher if you are going faster.
By inertia, the sliding body tends to move straight. The curved walls of the slide curve the path of the body. This force that changes the direction from the straight line is the centripetal force.
You slide higher because the walls are curved such a way that the greater radius of your turn allows a more straight motion to comply with the fact that your inertia moves you along a straight line.
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