Example 4: Newton's Second Law of Motion and Centripetal Force

https://3speak.tv/watch?v=mes/a95ab284 In this video, I go over the vector version of Isaac Newton's 2nd Law of Motion, which states that if a force F acts on a particle of mass m producing an acceleration a, then F = m a, where F and a are vectors in the same direction. I illustrate this with an example on an object moving in a circular path. The resulting force points in the opposite direction of the position vector, thus is always pointing inwards towards the origin. Such a force is called a centripetal or center-seeking force. I also illustrate the concept of angular speed, and how it and the radius effects the centripetal force by graphing it in the amazing GeoGebra 3D graphing calculator: https://www.geogebra.org/graphing/q7vx6myn #math #vectors #calculus #physics #Geogebra Timestamps: Isaac Newton's 2nd Law of Motion: F = m a – 0:00 Example 4: Centripetal Force – 0:53 Solution: First find the acceleration from the 2nd derivative of the position vector – 1:33 Force = mass times acceleration – 3:43 Force is negative and thus in the opposite direction of the position vector, so it points inwards toward the origin, and is called centripetal force – 4:50 Illustrating the centripetal force and angular speed – 6:20 Converting rectangular coordinates to polar coordinates – 8:43 Setting the polar angle as a function of its derivative, so that we have the angular speed as a variable of interest – 10:16 Inputs for GeoGebra 3D Graphing Calculator – 11:28 Graphing in GeoGebra – 14:01 Force gets bigger as radius is increased while angular speed is constant since the object has to speed up to maintain the constant angular speed – 17:29 Notes and playlists: 3Speak: SOON Summary: https://inleo.io/threads/view/mes/re-leothreads-2rb5fqugb Hive Notes: https://peakd.com/hive-128780/@mes/e443f9d3 Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0Hxo8aPU3ezG0tcLvgJnxLB . Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: [email protected] Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps