Solve Rotation Question Homework: Stop Space Capsule's 30 rev/min

[IWuvTeTwis]

Homework Statement

The figure shows the rear view of a space capsule that was left rotating rapidly about its axis at 30 rev/min after a collision with another capsule. You are the flight controller and have just moments to tell the crew how to stop this rotation before they become ill from the rotation and the situation becomes dangerous. You know that they have access to two small jets mounted tangentially, at a distance R = 3.0 m from the axis, as indicated in the figure. These jets can each eject 7.0 g/s of gas with a nozzle speed of 800 m/s. Determine the length of time these jets must run to stop the rotation. In flight, the moment of inertia of the ship about its axis (assumed constant) is known to be 5800 kg·m2.

The picture of the situation is attached.

Homework Equations

tau = I*alpha
tau = F x r
alpha*t = omega

The Attempt at a Solution

I can find the torque by taking 800m/s*2*7.0g/s*1g/1000kg*3.0m = tau
We are given I, so I can find alpha as well, alpha = 0.00579 1/s^2
Using that and the value for omega, I find that t = 9.04s which seems to be wrong.

Can anyone tell me what I'm doing wrong here?

 

[Filip Larsen]

Your value for alpha is correct, but the time is, as you suspect, not correct. Perhaps you have used wrong value for omega?