# 3-angular momentum : independent of pivot?

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1. Dec 3, 2014

### unscientific

1. The problem statement, all variables and given/known data

(i) Prove that dL/dt = 0
(ii) Find the relation between space part and 3-angular momentum vector
(iii)Show that 3-angularmomentum vector is independent of pivot

2. Relevant equations

3. The attempt at a solution

I'm not sure what part (iii) is trying to get at, but I think I've solved (i) and (ii):

Part(i)
$$\frac{\partial L^{ab}}{\partial \tau} = P^b \frac{\partial X^a}{\partial \tau} - P^a \frac{\partial X^b}{\partial \tau}$$

$$= \frac{P^bP^a}{m_0} - \frac{P^aP^b}{m_0} =0$$

Part(ii)
$$L_i = x_jp_k - x_kp_j$$

2. Dec 3, 2014

### unscientific

Solved it, thanks!