- #1

aim1732

- 430

- 2

[Vectors in bold]

**L**= Σ mi

**r**

_{i}×

**v**

_{i}

= Σ mi(

**r**

_{0}+

**r**

_{i,cm})×(

**v**

_{o}+

**v**

_{i,cm})

= Σmi

**r**

_{0}×

**v**

_{o}+ Σ

**r**

_{0}×(m

_{i}

**v**

_{i,cm}) + Σ(m

_{i}

**r**

_{i,cm})×

**v**

_{o}+ Σm

_{i}

**r**

_{i,cm}×

**v**

_{i,cm}...[1]

If the centre of coordinate system is at the centre of mass then by definition of centre of mass: Σm

_{i}

**r**

_{i}=0 and Σm

_{i}

**v**

_{i,cm}=0.

Now here's the the problem: terms 3 and 4 in [1] are zero in the centre of mass frame but the term 4 is not.But then using the same arguments I can say it is zero too. I am missing a point but can not point out what.