Model Airplane Nationals
Centripetal Acceleration?
The National Aeronautics and Space Administration (NASA) studies the physiological effects of large accelerations on astronauts. 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 8.9 times the acceleration due to gravity?
Using g = 9.80665 m/s², the desired centripetal acceleration for the astronaut is 8.9g = 87.2792 m/s²
The magnitude of a = ω²r, so ω = sqrt(a/r) = sqrt(87.2792 m/s² / 15 m) = 2.412 radians/s, or 2.4 radians/s with the correct number of significant digits.
If you want your answer in linear velocity of the chamber, v:
ω = v/r, so v = rω = 15 m * 2.412 radians/s = 36.1827 m/s, or v = 36 m/s with the correct number of significant digits.
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