determine the rotation rate, in revolutions per second, required to give the astronaut a centripetal acceleration of 19.0g

Question

the 20-g centrifuge at nasa's ames research center in mountain view, california, is a horizontal, cylindrical tube 58 ft long and is represented in the figure below. assume an astronaut in training sits in a seat at one end, facing the axis of rotation 29.0 ft away. determine the rotation rate, in revolutions per second, required to give the astronaut a centripetal acceleration of 19.0g.

Answer 1

Let

g = 32 ft/s² be gravitation acceleration,

r = 29 ft be the radius of rotation,

a = 19 g = 608 ft/s² be the desired acceleration,

ω be angular velocity (to be calculated).

The formula you need is

a = ω²r

Thus

ω = √(a/r)

The resulting ω will be in radians per second, but we want revolutions per second.

There are 2π radians per revolution, so

ω = √(a/r) / 2π = √(608/29) / 2π = 0.73 revolutions per second