It has been suggested that rotating cylinders about 16.0 mi long and 5.21 mi in

Question

It has been suggested that rotating cylinders about 16.0 mi long and 5.21 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth? A 59.0-kg ice skater is moving at 3.91 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around pole. Determine the magnitude of the force exerted by the horizontal rope on her arms. Compare the force with her weight.

Explanation / Answer

r = diameter/2 = 5.31 mi/2 = 5.31 x 1609.34 / 2 = 4272.8 m

centripetal acceleration is given as

ac = rW2

given that

ac = 9.8

rW2 = 9.8

4272.8 W2 = 9.8

W = 0.048 rad/s

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