Homework Statement
What is the relationship between the heat absorbed and rejected by the reservoirs and their temperature. If a heat pump is used to transfer heat what is the rate at which heat is added to the hot reservoir in terms of the temperatures of the reservoir and the work done by...
Ok I was wrong, but dr/dt cross itself goes to zero so:
\frac{dL}{dt}=\frac{d^{2}r}{dt^{2}}\times r?
I have to prove that \frac{d^{2}r}{dt^{2}} and r are in the same direction. Am I right in thinking that the very first equation shows exactly this? As both m and f(r) are scalars so do not...
Yes I know the product rules for cross products. So:
\frac{dL}{dt}=\frac{dr}{dt}\times\frac{dr}{dt}+\frac{d^{2}r}{dt^{2}}\times r
All the derivatives of and r itself are in the same direction so all go to 0 thus proving L is conserved :). Thanks for the help.
Homework Statement
The Force on a mass with position vector r satisfies:
m\frac{d^{2}\textbf{r}}{dt^{2}}=F=f(\textbf{r})\textbf{r}
where f(r) is scalar function of r. Show that L:
L=\textbf{r}\times\frac{d\textbf{r}}{dt}
is conserved.
Homework Equations
The Attempt at a...