Physics, From the Ground Up, Ep. 8: M3a · Angles and Radians

Description: Your little finger, held at arm's length, can hide the whole Moon. How? This video builds angles from scratch: what an angle measures and why a full turn is 360°, the circumference and the number π, arc length, and radians, the natural way to measure angles that physicists use everywhere. Then it measures the Moon with a single angle. Chapters: 0:00 A finger and the Moon 1:11 What an angle measures 3:27 Why 360? 5:09 Round the circle 7:02 Squeezing pi 9:19 Arc length 10:40 Radians 13:20 Why radians? 15:32 Turning speed 17:29 Small angles 19:31 Common mistakes 20:42 Recap and what's next WHAT YOU'LL LEARN • What an angle measures, and degrees: why 360 (Babylonian astronomy) • Circumference, C = 2πr, and how Archimedes and Zu Chongzhi pinned down π • Arc length as a fraction of the circumference • Radians: arc ÷ radius; converting; s = rθ • Angular speed: ω, and v = rω for wheels, records, washing machines and the Earth • The small-angle rule: size ≈ distance × angle; the Moon's size and why eclipses are so exact • Seven pause-and-try questions, with every step shown COMPANION WEBSITE Notes, key equations, sources, practice problems with full solutions, and further learning: https://relativelypuzzled.com/ground-... SOURCES • Why 360: the reason is uncertain; Babylonian astronomy; Hypsicles (2nd century BC) is the earliest surviving Greek use. • Archimedes, Measurement of a Circle, Proposition 3 (about 250 BC): π is greater than 3 10/71 and less than 3 1/7, using 96-sided polygons. • Zu Chongzhi (429–501): π is between 3.1415926 and 3.1415927; he also calculated 355/113. His book Zhui shu is lost (MacTutor). • Roger Cotes, Harmonia mensurarum (1722); "radian" first printed 5 June 1873 in exam questions by James Thomson, Queen's College Belfast. • Tony Hawk's first 900, X Games V, San Francisco, 27 June 1999 (Guinness World Records). • Moon and Sun data: NASA fact sheets. London Eye: 120 m wheel, about 30 minutes a turn. #maths #physics #geometry