All physics classes cover the formula for acceleration when the motion is in a circle. In an example usually given, the formula lets us compute the tension in a string when a mass at the end of the string is being spun in a circle.
Although the textbooks do not make a fuss over the formula, its discovery by Isaac Newton in 1655 was a landmark in the history of science. Deriving the formula required a great deal of insight into the nature of motion, and it was the starting point for Newton’s work on gravity and the motion of planets.
In this post, I will derive the formula using only basic mathematics, something physics courses do not usually do.

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Calvin and Hobbes cartoon, March 9, 2011

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