(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the form of Newton's Second Law is invariant under:

(a). a Galilean Transformation (GT) in 1-Dimension.

(b). a Galilean Transformation (GT) in 2-Dimensions.

(c). a Galilean Transformation (GT) in 3-Dimensions.

2. Relevant equations

Newton's Second Law.

[tex]

{{\sum_{}^{}}{\vec{F}}} = {m{\vec{a}}}{\,}{\,}{\text{[N.II.L.]}}

[/tex]

GT for 1-D

[tex]

{{x}^{\prime}} = {{x}-{vt}}

[/tex]

[tex]

{{y}^{\prime}} = {y}

[/tex]

[tex]

{{z}^{\prime}} = {z}

[/tex]

[tex]

{{t}^{\prime}} = {t}

[/tex]

GT for 2-D

[tex]

{{x}^{\prime}} = {{x}-{{v}{\left({\frac{x}{\sqrt{{x^2}+{y^2}}}}\right)}{t}}}

[/tex]

[tex]

{{y}^{\prime}} = {{y}-{{v}{\left({\frac{y}{\sqrt{{x^2}+{y^2}}}}\right)}{t}}}

[/tex]

[tex]

{{z}^{\prime}} = {z}

[/tex]

[tex]

{{t}^{\prime}} = {t}

[/tex]

GT for 3-D

[tex]

{{x}^{\prime}} = {{x}-{{v}{\left({\frac{x}{\sqrt{{x^2}+{y^2}+{z^2}}}}\right)}{t}}}

[/tex]

[tex]

{{y}^{\prime}} = {{y}-{{v}{\left({\frac{y}{\sqrt{{x^2}+{y^2}+{z^2}}}}\right)}{t}}}

[/tex]

[tex]

{{z}^{\prime}} = {{z}-{{v}{\left({\frac{z}{\sqrt{{x^2}+{y^2}+{z^2}}}}\right)}{t}}}

[/tex]

[tex]

{{t}^{\prime}} = {t}

[/tex]

3. The attempt at a solution

I'm not sure exactly where to begin here. Particularly, how to proceed in the: 2-D and 3-D; cases since I have extra variables to deal with in those GT equations.

Thanks,

-PFStudent

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# Homework Help: Modern Physics - Invariability of Newton's 2nd Law under a GT?

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