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## Interactive Lecture on Assumptions about Central Force Motion ( minutes)

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.
- 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;
- the force is central, i.e., the force acts along the line between the two particles and depends only on the distance between them.