# Calculating the Rotation Speed of a Trainee in a Training Device

## Understanding the Situation

A device for training astronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 11.0 m. The force felt by the trainee on her back is 7.25 times her own weight.

## Calculating the Rotation Speed

The centripetal force felt by the trainee on her back is equal to 7.25 times her weight, which can be represented as:

**F_c = 7.25W**

The centripetal force is given by the formula:

**F_c = ma_c = m * (v^2 / r) = m * ω^2 * r**

Replacing this and solving for the angular speed (ω), we get:

**m * ω^2 * r = 7.25mg**

**ω^2 = 7.25g / r**

**ω = √(7.25g / r)**

Substitute the values of acceleration due to gravity (g) and radius (r) into the formula:

**ω = √(7.25 * 9.8 m/s^2 / 11 m)**

**ω = 2.54 rad/s**

## Conclusion

The trainee is rotating at a speed of 2.54 radians per second in the training device.

What is the formula used to calculate the angular speed of the rotating trainee?

The formula used to calculate the angular speed of the rotating trainee is: ω = √(7.25g / r)