Using Integrals to Derive Rotational Inertia of a Long, Thin Rod with Demonstration

We use integrals to derive the #rotationalinertia of a uniform, long, thin rod. And we demonstrate our answer is correct using a Rotational Inertia Demonstrator. Want Lecture Notes? https://www.flippingphysics.com/thin-... This is an AP Physics C: Mechanics Topic. 0:00 Intro 0:15 Rotational Inertia 0:42 Linear Mass Density 1:51 About Center of Mass 3:02 About an End 4:27 Rotational Inertia Demonstrator (RID) 6:09 About Center of RID 7:03 Comparing our answers 7:43 Demonstrating our answer Next Video: 2 Masses on a Pulley - Torque Demonstration https://www.flippingphysics.com/2-mas... Multilingual? Please help translate Flipping Physics videos! http://www.flippingphysics.com/transl... Graphing the Rotational Inertia of an Irregular Shape https://www.flippingphysics.com/graph... Want a Rotational Inertia Demonstrator? https://www.arborsci.com/rotational-i... Previous Video: How the Force of Tension on a Pulley Changes with Acceleration https://www.flippingphysics.com/pulle... Please support me on Patreon!   / flippingphysics   Thank you to Christopher Becke for being my Quality Control Team for this video. http://flippingphysics.com/quality-co... Thank you to Jonathan Sullivan-Wood for transcribing the English subtitles of this video.