So to prove angular momentum (L = r x p) is conserved, I have to prove the derivative of L = 0.

The proof I have is the derivative of L

= (ṙ × p) + (r × ṗ)

= 0 + r × F

= 0

(Sorry about the formatting, really new here).

I don't understand

1) Why (ṙ × p) = 0

2) Why r × F = 0

Thank you so much sorry the formatting is terrible.