Deriving the Angular Momentum of a Particle: Proof of Differentiation

[solarei]

Homework Statement

Angular momentum of a particle is: L = (dr/dt) x mr

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

Homework Equations

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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.




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

 

[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:

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

?

 

[vela]

Homework Statement

Angular momentum of a particle is: L = (dr/dt) x mr

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.

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

Homework Equations

-----

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.

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

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

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

Basically, my knowledge on differentiation isn't up to par

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".

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.

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

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

 

[solarei]

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