Many particle system - problem with cross product

[lavster]

in a many particle system we have a center of mass R and position vector of the ith particle with respect to centre of mass is r_i. hence the position vector measured from the origin is R_i=R+r_i.

why does $$R\times\sum (m_i \dot{r}_i) =0$$, where $$\dot{r}_i$$ denotes the rate of change wrt time and m_i is the mass of the ith particle?

thanks

 

[tiny-tim]

hi lavster!

(have a sigma: ∑ and try using the X² tag just above the Reply box )

because by definition of centre of mass,

∑ m_ir_i' = (∑ m_ir_i)' = 0'