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and that is the internal motion relative to the center of mass? could give me some examples? desire to relate since I need to find out what is the kinetic energy in the center-of-mass of two particles, one moving and one stationary. Note: they collide

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The center of mass of a two-particle system is, by definition, at position

$$x_\textrm{com} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}.$$

The relative position of your particles relative to the CoM can be found by substracting the position of the CoM:

$$x'_1 = x_1 - x_\textrm{com},\ x'_2 = x_2 - x_\textrm{com}.$$

That should help you get started. Try differentiating those expressions to come up with how velocities relate, and what the kinetic energy would be.

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