# Gyroscope on rotating disk

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1. Nov 14, 2015

### kontejnjer

1. The problem statement, all variables and given/known data
Describe the motion of a gyroscope with center of mass fixed on a rotating disk in coordinates of an observer which is at rest on the disk in the absence of gravity.

2. Relevant equations
The hint given was to somehow use Fermi transport, so I'm guessing:
$\mathbb F_u X=\nabla_u X-\left<X,\nabla_u u\right>u+\left<X,u\right>\nabla_u u$

3. The attempt at a solution

I honestly have no clue. I suppose since $u$ is timelike and $X=S$ should be spacelike, the last term on the right side goes away. Can we also assume we Fermi transport $S$ along a curve (is this the curve the gyroscope traces out? My notes just say a "timelike curve" so it's not very clear) $\gamma(s)=\left(t(s),\cos\varphi(s),\sin\varphi(s)\right)$ with $\dot\gamma=u$, so $\mathbb F_u S=0$? I find this whole Fermi transport thing very confusing, so any tips or hints would be useful, I've been staring at this problem for days now and sadly made no significant progress.

2. Nov 19, 2015