This was writen on the board this last semester, and I cant seem to figure it out and its been bothering me to no end (mentally).(adsbygoogle = window.adsbygoogle || []).push({});

Momentum is defined as:

[tex]p=mv[/tex]

therefore, if you want to find the differential momentum, itshouldbe, mathematically speaking:

[tex] d(p)=d(mv)=dp=dm*V+m*dV[/tex]

But differetial momentum is always writen as:

[tex] dp=dm*V[/tex]

I cant make sense out of what happened to the second term on the right side.

In fluid mechanics we have:

[tex]d(\rho VA)=\frac{d \rho}{\rho}+\frac{dV}{V} +\frac{DA}{A}[/tex]

So d(p) for momentum should follow just the same using the product rule.

It makes sense conceptually, as each particle dm has a velocity V, and if you sum it over the body you get the total momentum, but it seems totallywrongmathematically.

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# Momenum and differential of momentum

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