# Angular Momentum Torque

1. May 4, 2012

### naestibill

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

Considering the concepts of Rigid Body/Angular Momentum/Torque
A body rotating with respect to an axis that passes through ANY point P, whose acceleration could be different to zero.

Prove:

Ʃτ(ext, p) = dL(rel_p)/dt + ρ(cm) x Ma(p)
Ʃτ(ext, p) = dL(rel_cm)/dt + ρ(cm) x Ma(cm)

2. Relevant equations

T = dL/dt
L = Ʃ ρ x mv

3. The attempt at a solution
Considering a Rigid Body/Angular Momentum/Torque

We know that Torque(ext) = dL/dt

Now with respect to stationary point S:
L(s, cm) = Ʃ(ρi x mivi)
and that dL(cm)/dt = Ʃτ(ext, CM)

Now with respect to ANY point, P, that is accelerating:
L(s,p) = L(cm) + ρ(cm) x Mv(cm)

after this I don't know how to prove what they are asking me for

2. May 4, 2012

### D H

Staff Emeritus
The motion of a rigid body can be described as a combination of linear translation/acceleraion of some point plus a rotation/rotational acceleration about an axis passing through that point. So what is that "some point"? It can be any point whatsoever -- and that is what you are being asked to prove.