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| 183_notes:sep_k_ex [2014/11/01 14:36] – caballero | 183_notes:sep_k_ex [2014/11/01 14:40] (current) – caballero | ||
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| ===== Formal derivation of $K_{trans}$ and $K_{rel}$ ===== | ===== Formal derivation of $K_{trans}$ and $K_{rel}$ ===== | ||
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| In the notes, you will read about the formal derivation to separate the total kinetic energy into a translational component that tracks the energy associated with the motion of the center of mass, and the relative component that that tracks the energy of due to the motion relative to the center of mass. | In the notes, you will read about the formal derivation to separate the total kinetic energy into a translational component that tracks the energy associated with the motion of the center of mass, and the relative component that that tracks the energy of due to the motion relative to the center of mass. | ||
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| Begin by considering two particles, one of mass $m_1$ at location $\vec{r}_1$ measured relative to some fixed coordinate axes and the other of mass $m_2$ at location $\vec{r}_2$ measured relative to the same coordinate axes. Both of these vectors positions are indicated with grey arrows. | Begin by considering two particles, one of mass $m_1$ at location $\vec{r}_1$ measured relative to some fixed coordinate axes and the other of mass $m_2$ at location $\vec{r}_2$ measured relative to the same coordinate axes. Both of these vectors positions are indicated with grey arrows. | ||
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| For these two particles, we could determine their center of mass, | For these two particles, we could determine their center of mass, | ||