What frequency of rotation, in rpm, is required to give an acceleration of 1.4 g to an astronaut's feet, if her feet are 1.6 m from the platform's rotational axis

The frequency of rotation of the platform is approximately 27.970 revolutions per minute.

Explanation:

In this case, the astronaut experiments a centrifugal acceleration as a reaction to the centripetal acceleration due to the rotation of the platform. (Second and Third Newton's Laws). Centripetal acceleration (), measured in meters per second, is expressed as:

(Eq. 1)

Where:

- Angular velocity, measured in radians per second.

- Distance of the astronaut's feet from the rotational axis of the platform, measured in meters.

Now we clear the angular velocity:

If we know that and , the angular velocity of the platform is:

And this outcome is converted into revolutions per minute:

The frequency of rotation of the platform is approximately 27.970 revolutions per minute.

v=ir = 3x15 =45 v