# Proof of differentiation

1. Sep 12, 2014

### solarei

1. The problem statement, all variables and given/known data
Angular momentum of a particle is: L = (dr/dt) x mr

Show that (dL/dt) = (d2r/dt2) x mr

2. Relevant equations
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3. The attempt at a solution

My atempt is that I tried writing it in the form y = mx + c but I don't think that would be relevant.

Next I tried straight forward rule application derivision (it was wrong to try that)

Basically, my knowledge on differentiation isn't up to par and so far I haven't tried integrating it but I seriously doubt it'd lead to the answer and I don't know how to apply an intergral of (dL/dt) to the mr term.

I've also considered writing r = irx + iry + irz but again, no idea how to apply it in equation.

2. Sep 12, 2014

### Matterwave

Do you know the product rule of differentiation? You can apply it to a cross product too. For example, would you be able to do this:

$$\frac{d}{dt}(\vec{A}\times\vec{B})$$

?

3. Sep 12, 2014

### vela

Staff Emeritus
Are you sure this is correct? Angular momentum is usually defined as $\vec{L} = \vec{r}\times\vec{p}$, where $\vec{p}=m\vec{v}$ is the momentum. It differs from your definition by a sign.

Tried writing what? What's "it" supposed to be?

What rule? What's "derivision"? I'd guess you mean differentiation, but you used the word differentiation correctly below so perhaps not.

Good, you identified a problem. Now you need to do something to fill the gap in your knowledge. Did you check your book for a similar example? Perhaps there's an appendix that covers or reviews some math. You could try googling "differentiating a cross product".

Yeah, you're trying to calculate a derivative, so integrating likely isn't going to help.

4. Sep 14, 2014

### solarei

Actually, going over some notes, I can see where errors were made, sorry about that.