1) The National Aeronautics and Space Administration (NASA) studies the physiolo

Question

1) The National Aeronautics and Space Administration (NASA) studies the physiological effects of large accelerations on astro-nauts. Some of these studies use a machine known as a centrifuge. This machine consists of a long arm, to one end of which is attached a chamber in which the astronaut sits. The other end of the arm is connected to an axis about which the arm and chamber can be rotated. The astronaut moves on a circular path, much like a model airplane flying in a circle on a guideline. The chamber is located 15 m from the center of the circle. At what speed must the chamber move so that an astronaut is subjected to 7.5 times the acceleration due to gravity?

Explanation / Answer

Let the angular speed be w ...

The acceleration is given by : a = w^2 * r

where r = radius = 15 m ..

given a = 7.5 g = 7.5 * 9.8

so...

7.5 * 9.8 = w^2 * 15

so w = 2.2136 rad / sec

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