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Question

NASA's Ames Research Center in Mountain View, California, houses a 20g centrifuge used to conduct research and training to solve real world problems related to the effects of acceleration on systems. It consists of a horizontal rail system with a 58-foot diameter mounted on a central axis, as shown in the figure below. An astronaut is using the centrifuge for training on high accelerations during spaceflight. The astronaut is seated 29.0 ft from the axis of rotation. At what rotation rate, in revolutions per second, will the astronaut experience a centripetal acceleration of 16.8g?

:______rev/s

Answer 1

The relevant equation is from centripetal acceleration.

a_c=v²/r.

If we can solve for v, we can use this to calculate the angular velocity...

v=sqrt(a_c*r)

We can relate velocity to angular velocity with the following relationship...

v=ωr

Plugging this in to our equation...

ωr=sqrt(a_c*r)

Now we solve for ω...

ω=sqrt(a_c/r)

Now, we plug in the numbers (note I changed the radius into meters)...

ω=sqrt(16.8*9.8/8.8392)=4.3158 rad/s

Finally, we convert from rad/s to rev/s...

ω=4.3158/(2π)=0.6869 rev/s

ω=0.6869 rev/s