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11.3: Law of Addition of Velocities - Newtonian Mechanics

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    Suppose the object in Figure 11.1 is moving; then observers in different reference frames will measure different velocities. Denote the velocity of the object in frame \(S\) by \(\overrightarrow{\mathbf{v}}=d \overrightarrow{\mathbf{r}} / d t\), and the velocity of the object in frame S′ by \(\overrightarrow{\mathbf{v}}^{\prime}=d \overrightarrow{\mathbf{r}}^{\prime} / d t^{\prime}\). Since the derivative of the position is velocity, the velocities of the object in two different reference frames are related according to

    \[\frac{d \overrightarrow{\mathbf{r}}^{\prime}}{d t^{\prime}}=\frac{d \overrightarrow{\mathbf{r}}}{d t}-\frac{d \overrightarrow{\mathbf{R}}}{d t} \nonumber \]

    \[\overrightarrow{\mathbf{v}}^{\prime}=\overrightarrow{\mathbf{v}}-\overrightarrow{\mathbf{V}} \nonumber \]

    This is called the Law of Addition of Velocities.

    This page titled 11.3: Law of Addition of Velocities - Newtonian Mechanics is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Peter Dourmashkin (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.