IF you could dig a tunnel from London UK to Sydney AUS through the centre of the earth and jumped in would you fall out or climb out ... (Hypertheticaly)
Good question. I have often thought about this and have looked into it before and the best answer I can give you is, I don't know. It mashes my head up trying to think about it.
Maybe you would just spin at the centre of the Earth, trapped between 2 gravitational pulls.
you would fall to the centre of the earth however once you reach there there's no gravity so you would only continue due to momentum, once moving into the other side of the earth gravity would act in the opposite direction( back to the centre) so you would have to climb the rest of the way out.
When you reached the centre of the earth you would, as John89 says, shoot past it under your momentum. But when you then slowed and stopped you would start falling again - back towards the centre of the earth, of course. Possibly another, smaller, overshoot and another reverse of direction, causing you to oscillate for a while before settling at the centre for ever.
Ignoring, of course, that you'd have been burnt to a frazzle by molten iron long before.
If you jump into such a tunnel you would be in oscillation with London and Sydney as the extremes and the centre of the earth a your mean for ever (if of course there is no friction due to the air).This situation is pretty much like a pendulum where gravity acts like the tension (the restoring force) the of the string.
Robb Phoenix, why on earth (sorry, in earth!) would you oscillate for ever?
What would power you? A pendulum, don't forget, needs powering to keep it going.
You would oscillate with decreasing amplitude until you eventually came to rest at the centre.