Teaching Physics (and more) with Niven

Notes

It’s widely understood that pseudogravity can be produced by rotation, but it’s educational to use Ringworld as a way to demonstrate why. If a person holding an object a distance h above the surface of the Earth and drops it, it hits the ground after this amount of time – the square root of 2 times the height divided by g (so it takes about 1 second for an object to fall 16 feet). On the Ring, when the object is dropped, the motion is determined by the following equations – the object doesn’t move at all in the y direction, while the object retains its motion in the x direction. The square of the total distance from the center is the sum of squares of the x and y values – and what we care about is the moment when the square of the distance equals R squared. Solving for t gives the square root of 2 times (R*h), so the equivalent acceleration of gravity on Ringworld is v squared over R. Similar calculations comparing how high an object gets when you throw it upward with a given velocity give the same answer for equivalent gravity. Note that we’ve approximated the answer – so as h becomes a significant fraction of R, Ringworld gravity stops being so similar to Earth’s. For example...

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