# Homopolar generator

^{2}B.

I need to find the time taken for the disc to slow to half it’s initial speed ignoring friction, given a resistance R is connected between centre and rim and all other circuit resistance is negligible. It has mass m.

So I know it’s moment of inertia is 0.5ma^{2}, and that energy is conserved such that the difference in the rotational KE initially and finally equals the energy dissipated in the resistance. This energy E is

E=0.5Iw^{2}-0.5I(0.5w)^{2}

E=0.5Iw^{2}-0.125Iw^{2}

E=(3/8)(0.5ma^{2})w^{2}

E=(3/16)ma^{2}w^{2}

Now comes the problem in calculating the energy dissipated in the resistance. Obviously the induced emf and so induced current are time dependent. I’m not sure how I can get expressions for these in terms of time such that I could get the power dissipation with time and integrate for the energy. Any clues please? Thanks ðŸ™‚

http://ift.tt/1dB3HR1

## Leave a comment