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

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 .

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