For the film 2001 Space Odyssey, director Stanley Kubrick had a giant centrifuge constructed, of diameter 11.6 m. On the movie set, motors rotated the centrifuge about a horizontal axis, like a Ferris wheel. This was the home for fictional astronauts on their long journey to the planet Jupiter, providing artificial gravity throughout the trip.

(a) In one scene, astronaut Dr. Frank Poole is seen jogging all the way around the circumference of the centrifuge, requiring about \(25 \mathrm{~s}\) to do so. What was the rotational period of the centrifuge on the movie set, and how fast was he jogging?

(b) In the movie, it appears that Poole is jogging in a gravity approximately the same as on earth. (No surprise!) Assuming that \(g_{\text {effective }}=g_{\text {earth }}\) while standing at rest on the centrifuge rim, and that the centrifuge was actually rotating on the spaceship en route to Jupiter, what would the rotational period of the centrifuge have to be?

(c) Suppose the movie astronaut was \(1.9 \mathrm{~m}\) tall. By what percentage less would the artificial gravity be on his head than on his feet, just standing on the centrifuge rim?

(d) Would it make any difference if the fictional astronaut were jogging in the direction of rotation or opposite to it? If so, what would be the effect of jogging in the two directions?