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Radians

Ian Harding explains how the radian unit of angular measurement is defined, and shows how radians are used in mathematical descriptions of oscillations and waves

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Have you ever wondered why there are 360 degrees in a circle? I suspect not — you are so familiar with the degree as the unit for angles that you may never have thought about why we use them. On the other hand, 360° does not seem to sit well with all the other units you are familiar with in physics. Most of the measurements we use are based on powers of ten — they are metric (or decimal) units — and physicists tend to use SI (Système International) units.

When the French were busy inventing the metric system from about 1799 an attempt was made to create a metric form of angular measurement. The right-angle was divided into 100 grads, or grades, and each of these was further subdivided into 100 centigrades — with the obvious risk of confusion with a popular name for the degree Celsius. Although 100 is a metric (power of ten) number a complete circle of four right-angles would total 400 grads, and this doesn’t seem very metric at all.

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Previous

Explaining electromagnetic induction

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Solution and notes

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