Centripetal force is the force that holds an object moving in a circular path. For cars, the force of friction provides centripetal force so the car can turn. For the moon, gravity between the earth and moon holds the moon in place. Centripetal force can be the result of many different forces, but there are a few basic steps to follow to calculate centripetal force.
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Calculating Centripetal Force

Find the mass of the object that is moving in the circular path in kilograms, the radius of the circular path, and the speed of the object. For example, the mass of a car might be 1,000 kilograms. A car may turn a corner while following a circular path of radius 20 meters at a speed of 15 meters per second.

Find the square of the speed of the object. In our example, the square of the speed would be 225.

Multiply the square of the speed by the mass of the object. In our example, we would multiply 225 from the previous step by 1,000 for a result of 225,000.

Divide the product from the previous step by the radius of the circular path. This number is the centripetal force in Newtons needed to hold the object in a circular path. For our example, we would divide 225,000 by 20 to get 11,250 Newtons.

Check your units to make sure they turn out to be Newtons or some other unit of force. In our example, we multiplied kilograms by meters squared per second squared (the square of the velocity) and divided by meters, giving us kilograms meters per second squared, otherwise known as Newtons.
Tips & Warnings
 Pay attention to the units. If you multiply by grams instead of kilograms, your answer is going to be way off. Write out each step. You are less likely to make a mistake if you write everything out.
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References
 Douglas Giancoli, Physics, fifth edition, 2002, Prentice Hall
 Centripetal Force