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Suppose Earth's spin angular velocity were increased until objects at the equator just began to float (become weightless). Approximately how long would a day then last? (g = 10 m/s², Earth radius R = 6400 * 10³ m, pi = 3.14)

1. 60 minutes
2. does not change
3. 1200 minutes
4. 84 minutes

Correct answer: 84 minutes

Solution

Bodies float when their weight is fully used as centripetal force: m*g = m*omega²*R, so omega = sqrt(g/R). The day length is T = 2*pi/omega = 2*pi*sqrt(R/g). Plugging in values gives about 5060 s, roughly 84 minutes.

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