Consider a particle of mass $m$ having linear momentum $\vec{p}$ at position $\vec{r}$ relative to the origin $O$. Let $\vec{L}$ be the angular momentum of the particle with respect to the origin. Which of the following equations correctly relate $\vec{r}, \vec{p}$ and $\vec{L}$?

• A
  $\frac{d\vec{L}}{dt} + \vec{r} \times \frac{d\vec{p}}{dt} = 0$
• B
  $\frac{d\vec{L}}{dt} + \frac{d\vec{r}}{dt} \times \vec{p} = 0$
• C
  $\frac{d\vec{L}}{dt} - \frac{d\vec{r}}{dt} \times \vec{p} = 0$
• D
  $\frac{d\vec{L}}{dt} - \vec{r} \times \frac{d\vec{p}}{dt} = 0$