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 20.0 m from the center of the circle. At what speed must the chamber move so that an astronaut is subjected to 5.64 times the acceleration due to gravity

w = 1,662 rad / s,    v = 33.25 m / s

Explanation:

This this exercise indicates that the acceleration felt by the astronauts is

         a = 5.64 g

in a circular motion the centripetal acceleration is

        a_c = v²/ r

angular and linear variables are related

         v = w r

we substitute

        a_c = w² r

we finally have

         5.64 g = w² r

         w² = 5.64 g / r

let's calculate

         w =

         w = 1,662 rad / s

linear velocity is

        v = w r

        v = 1,662 20

         v = 33.25 m / s

the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.