Quote by pff
Thanks for the reply, but the idea of the centrefuge has confused me even more.
Wouldn't we get the same result by summing before integrating rather than after? (comparing the two methods i outlined in the first post)

You spoke of taking the euclidean distance and subtracting 9.81 from that. That's not a vector subtraction. That's a scalar subtraction. That means you would not be integrating a vector. You would be integrating a scalar, completely ignoring the direction of the acceleration.
The point I was trying to make is that you need to subtract the 9.81 as a vector, leaving a residual vector acceleration and integrate that.
The centrifuge example would have a high scalar acceleration. Integrate that and you get a huge number. But integrate the vector and the directions would tend to cancel out over the long run giving a much lower number.
Did I make sense that time or am I still losing you?