# Derive total angular momentum for the collection of particles

So I was trying to figure out how the total angular momentum for the collection of particles is derived. Here in Wikipedia https://en.wikipedia.org/wiki/Angular_momentum#Center_of_mass is the derivation, but there is this one part that I do not understand. How does the term

$$\sum_ir_i\times m_iV$$

vanish? I also know that $$\sum_i m_ir_i=0$$, but how does that help making the term vanish?

• Oct 4 '19 at 13:37

## 1 Answer

Rearrange the above equation as $$\sum_i m_ir_i \times V$$. Notice that this is the same as $$m_i$$ is a scalar. Now, $$V$$ is a constant vector in the above equation. We know that $$\sum_i m_ir_i$$ is $$0$$. So multiplying both sides by a constant vector is also $$0$$.