Electric Dipole in a Magnetic Field: Conservation of energy

[sparkle123]

Please help me with the attached question.

I don't understand how you get from the first line to the second line in (2). (I'm not too familiar with working with cross products and vectors).

Also, I don't know how you get (5) from (1) and (2).

Any help would be much appreciated. Thanks! :)

 

[dikmikkel]

(2) the equality Comes from $\vec{v}_{cm} = \dfrac{1}{2}(\vec{v}_1+\vec{v}_2)$
(5) Try to wite down the full expression $E = \dfrac{1}{2}mv_{cm}^2+\dfrac{1}{2}I\omega^2$
Using (1) and (2)
And take the time derivitative(here dE/dt is indicated with a small dot above). Then you would see that the energy is conserved.

 

[sparkle123]

Thanks dikmikkel! :)