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Summary of the Equation for the Magnitude of Centripetal Force Felicia Cherry Product Manager for Physical Science, Physics, and Earth Science Almost every physics class covers circular motion. Students spend considerable time learning the basic formula and solving problems. This article describes an algebra-based derivation of the equation for centripetal force. Deriving the equation This first equation should be familiar.

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It is probably the most used equation in any first-year physics course and the way most physics students learn to express Newton’s Second Law: Equation 1. The net force on an object is equal to the mass of the object times the acceleration of the object. Equation 2 applies this principle to objects moving in uniform circular motion, where the object moves at a constant speed but continues to change direction so that it travels in a circular path. An object moving in uniform circular motion is acted on by a force directed at the center of the circular path, called a centripetal force. Equation 2 restates Equation 1 for objects moving in uniform circular motion.

F c stands for centripetal force, and a c stands for centripetal acceleration. The equation for the magnitude of centripetal force is given by: Equation 3.

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When describing linear motion, acceleration is usually described as the change in velocity divided by the change in time. Mathematically, acceleration may be expressed like this: Equation 4. From Equation 2 and Equation 3, centripetal acceleration, or a c, can be expressed as: Equation 5. The next section will explain why centripetal acceleration is equal to velocity squared divided by the radius, as written in Equation 5.