Thread: Angular Momentum

1. Angular Momentum

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.

2. Re: Angular Momentum

Originally Posted by princessp
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.
Look at the directions of the vectors.

$\displaystyle \dot{r} \times p = v_{tan} \times mv$ where $\displaystyle v_{tan}$ is the tangential component of the velocity. What is the term v_{tan} x v equal to?

$\displaystyle r \times F = r \times F_c$. What direction does the centripetal force have?

-Dan