Question

In the Hugo Award winning novel, Ringworld by Larry Niven, aliens build a massive ring in space for "people" to live on. [Halo is just a rip-off of Ringworld, IMO] The 186 million mile diameter ring surrounds a star for light and energy. People inhabit the inside of the ring which is spun to simulate gravity. (a) How fast would the ring have to spin in order for your measured "weight" to be the same as it is on Earth? (b) On the Earth you are also moving in a big circle as the planet spins. Shouldn't we be taking centripetal force ideas into account when we do the summation of forces on, let's say, you standing on the ground? Let's see ... first calculate how fast you are moving as the Earth spins. [Planetary data is on the Constants and Conversions Sheet.] (c) Next, calculate your centripetal acceleration because of the rotation of Earth and compare this value to the gravitational acceleration of Earth. Make sure to comment on why we don't need to take centripetal force into account.

Answer 1

a) If the velocity of the spining of ring is V then

mV²/R = mg

given R = (186*10^{6}*1609.34)/2 m

$=> V = \sqrt{Rg} = \sqrt{\frac{186*10^{6}*1609.34}{2}*9.8} = 3.87*10^{5} m/sec$

b) If V is the spped by which Earth is moving then

$V = \frac{2\pi R_{Earth}}{T} = \frac{2*3.14* 6400*10^{3}}{24*3600} =465.2 m/s$

c)

Centripetal acceleration = V²/R =465.2²/(6400*10³) = 0.034 m/s²