Consider a system of \(N\) particles whose coordinates are \(\mathbf{r} = \{r_i^x, r_i^y, r_i^z\}\), and whose velocities are \(\{\dot{\mathbf{r}}_i\}\).

Each pair of particles \(\left(i, j\right)\) interacts through a potential \(V\left(\mathbf{r}_i, \mathbf{r}_j\right)\) which has no direct dependence on time. As the system evolves in time, which of the following bulk quantities must be conserved?

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