Central Forces Notes Section 5

• Newton's Law Equations are written down for the motion of two interacting particles.

$$m_1\dfrac{d^2}{dt^2}\vec{r}_1=\vec{F}_{1,ext}-\vec{f}_{12}$$ $$m_2\dfrac{d^2}{dt^2}\vec{r}_2=\vec{F}_{2,ext}+\vec{f}_{12}$$

• Students work in groups to create a list of assumptions that were made in writing these equations
  • only 2 particles
  • same origin
  • masses do not change with time
  • all of Newton's laws apply
    • non-quantum (size)
    • non-relativistic (speed)
• These equations were added to find center of mass and are now subtracted to find relative motion.
• Discuss further assumptions that the class will use when dealing with central force problems.
  1. that you can ignore external forces since you only care about the relative motion of the particles, i.e., the motion of the particles with respect to the center of mass;
  2. the force is central, i.e., the force acts along the line between the two particles and depends only on the distance between them.