A device for training astronauts and jet fighter pilots is designed to move the trainee in a horizontal circle of radius 11.0 m. If the force felt by the trainee is 7.45 times her own weight, how fast is she revolving? Express your answer in both m/s and rev/s

When a body rotates in a horizontal circle, then the force felt by the body is known as centripetal force, whose magnitude depends on the velocity, radius, and mass of the body.

The radius of circle is \(r = 11\;{\rm{m}}\).

The equation of force felt by trainee is,

\({F_C} = \frac{{m{v^2}}}{r}\)

Here, m is the mass, v is the velocity, and r is the radius.

The given condition is,

\({F_C} = 7.45W\)

Here, W is the weight.

Substitute all the values in above equation,

\(\begin{aligned}\frac{{m{v^2}}}{r} &= 7.45mg\\v &= \sqrt {7.45rg} \\v &= \sqrt {7.45\left( {11\;{\rm{m}}} \right)\left( {9.8\;{\rm{m/}}{{\rm{s}}^2}} \right)} \\v &= 28.34\;{\rm{m/s}}\end{aligned}\)

Thus, the speed of astronaut in m/s is \(28.34\;{\rm{m/s}}\).

The speed in rad/s can be calculated as,

\(\begin{aligned}v &= r\omega \\v &= r\left( {2\pi N} \right)\\28.34\;{\rm{m/s}} &= \left( {11\;{\rm{m}}} \right)\left( {2\pi } \right)N\\N &= 0.41\;{\rm{rev/s}}\end{aligned}\)

Thus, the speed in rad/s is \(0.41\;{\rm{rev/s}}\).