- #1
AStaunton
- 105
- 1
looking at my notes on pulsars I have:
[tex]K=\frac{2\pi^{2}I}{P^{2}}\implies dk=\frac{2\pi^{2}I}{P^{2}}dP\implies\frac{dk}{dt}=\frac{-4\pi^{2}I}{P^{3}}\frac{dP}{dt}[/tex]
where K is kinetic rotational energy and P is momentum...
I don't quite follow the final expression (when the time derivitive is taken), when this is done to the final equality, it feels like the chain rule should be used as both dP and 2pi^2I/P^2 are functions of t...clearly I'm mistaken but I don't see why..I'm saying that I would have expected:
[tex]\frac{dk}{dt}=\frac{-4\pi^{2}I}{P^{3}}dP+\frac{2\pi^{2}I}{p^{2}}\frac{dP}{dt}[/tex]
[tex]K=\frac{2\pi^{2}I}{P^{2}}\implies dk=\frac{2\pi^{2}I}{P^{2}}dP\implies\frac{dk}{dt}=\frac{-4\pi^{2}I}{P^{3}}\frac{dP}{dt}[/tex]
where K is kinetic rotational energy and P is momentum...
I don't quite follow the final expression (when the time derivitive is taken), when this is done to the final equality, it feels like the chain rule should be used as both dP and 2pi^2I/P^2 are functions of t...clearly I'm mistaken but I don't see why..I'm saying that I would have expected:
[tex]\frac{dk}{dt}=\frac{-4\pi^{2}I}{P^{3}}dP+\frac{2\pi^{2}I}{p^{2}}\frac{dP}{dt}[/tex]