Uploaded April 2026 | Updated September 2026, 3 weeks ago
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: 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: 3speak.tv/watch?v=mes/a95ab284
- Summary: inleo.io/threads/view/mes/re-leothreads-2rb5fqugb
- Hive Notes: peakd.com/hive-128780/@mes/e443f9d3
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0Hxo8aPU3ezG0tcLvgJnxLB .
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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: 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: 3speak.tv/watch?v=mes/a95ab284
- Summary: inleo.io/threads/view/mes/re-leothreads-2rb5fqugb
- Hive Notes: peakd.com/hive-128780/@mes/e443f9d3
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0Hxo8aPU3ezG0tcLvgJnxLB .
------------------------------------------------------
Become a MES Super Fan! 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: peakd.com/@mes
Email me: contact@mes.fm
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
