How Does Angular Momentum Conservation Apply to Rotational Systems?

[cupid.callin]

Homework Statement

The Attempt at a Solution

I did it like this:

$$\vec{L}_{B \ wrt \ Ground} = \vec{L}_{B \ wrt \ A} + \vec{L}_{A \ wrt \ Ground}$$

$$\vec{L}_{B \ wrt \ A} = \vec{L}_{B \ wrt \ Ground} - \vec{L}_{A \ wrt \ Ground}$$

so

$$\vec{L}_{B \ wrt \ A} = mwd^2 \ - \ \frac{1}{4}mwd^2$$

$$\vec{L}_{B \ wrt \ A} = \frac{3}{4}mwd^2$$

why is my method wrong?

 

[tiny-tim]

hi cupid.callin!

$$\vec{L}_{B \ wrt \ A} = \vec{L}_{B \ wrt \ Ground} - \vec{L}_{A \ wrt \ Ground}$$

sorry, but this doesn't work at all

L_A(B) = r_AB x (v_B - v_A)

= (r_OB - r_OA) x ((v_B - v₀) - (v_A - v_A)) …

bits of that are the RHS of your equation, but that's all

 

[cupid.callin]

Why is does not work,

Is it because the eqn i used relates velocity or acceleration of particle wrt to a non inertial particle or frame ?

 

[tiny-tim]

why should it work?

it obviously doesn't work …

the RHS of your equation is r_OB x v_B - r_OA x v_A