- #1
Cyrus
- 3,238
- 17
This was written on the board this last semester, and I can't seem to figure it out and its been bothering me to no end (mentally).
Momentum is defined as:
[tex]p=mv[/tex]
therefore, if you want to find the differential momentum, it should be, mathematically speaking:
[tex] d(p)=d(mv)=dp=dm*V+m*dV[/tex]
But differetial momentum is always written as:
[tex] dp=dm*V[/tex]
I can't 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 totally wrong mathematically.
Momentum is defined as:
[tex]p=mv[/tex]
therefore, if you want to find the differential momentum, it should be, mathematically speaking:
[tex] d(p)=d(mv)=dp=dm*V+m*dV[/tex]
But differetial momentum is always written as:
[tex] dp=dm*V[/tex]
I can't 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 totally wrong mathematically.