Classical Mechanics | 5.3: Deriving v = rω from Chord Length and Small Angles

Full course — free exercises, Feynman reviews, and AI-graded feedback: https://ludium.ai/courses/classical-m... One little formula governs the speed of anything spinning on a string: v equals r times omega. This video derives it from pure geometry, using the chord of an arc, an isosceles triangle, and the small-angle approximation, then shows which way the velocity points. Key concepts covered: The chord between two position vectors on a circle The isosceles triangle and the chord-length formula The small-angle approximation in radians and how negligible the error is Speed as the limit of chord over time: v equals r times omega The direction of the velocity vector around the circle ━━━━━━━━━━━━━━━━━━━━━━━━ SOURCE MATERIALS The source materials for this video are from https://ocw.mit.edu/courses/8-01sc-cl...