On a Lemma of the Shell Theorem

1. Jan 13, 2012

TMO

I am concerned regarding a lemma of the shell theorem. Specifically, I am concerned with the idea that due to the vector nature of the forces, that one can simplify this:

into this:

Could somebody precisely explain why we're allowed to multiply in the $\cos \varphi$ in the second equation?

2. Jan 13, 2012

maverick_starstrider

It's a dot product with the radius unit vector. You're projecting the contribution of dF (which I'm inferring is along s) along the radius vector r