21.2: Translational Equation of Motion
- Page ID
- 25642
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We shall think about the system of particles as follows. We treat the whole system as a single point-like particle of mass \(m_{T}\) located at the center of mass moving with the velocity of the center of mass \(\overrightarrow{\mathbf{V}}_{c m}\) The external force acting on the system acts at the center of mass and from our earlier result (Equation 10.4.9) we have that
\[\overrightarrow{\mathbf{F}}^{\mathrm{ext}}=\frac{d \overrightarrow{\mathbf{p}}_{\mathrm{sys}}}{d t}=\frac{d}{d t}\left(m_{T} \overrightarrow{\mathbf{V}}_{c m}\right) \nonumber \]