Stopping Rotation of Space Capsule: How Long Do the Jets Need to Run?

[Vanessa23]

Homework Statement

A space capsule was left rotating rapidly about its axis at N = 34.0 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 = 3.11 m from the axis, as indicated in the figure. These jets can each eject 13.7 g/s of gas with a nozzle speed of v = 712 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 3872 kg·m2.

Homework Equations

rotational momentum of station = angular momentum of the jets
--> rotational momentum of station = (moment of intertia)*(angular velocity)
--> angular momentum of jets = (mass)(speed)(radius)

The Attempt at a Solution

--> therefore (momentum of inertia)*(angular velocity) = (mass)*(speed of gas ejected)*(distance from axis)

--> mass divided by the grams/second of gas = seconds needed
--> then divide that answer by 2 because there are 2 jets

(3872*3.56rad/s)/(.0137*3.11)= 3.24x10^5 kg
3.24x10^5 /.0137= 2.36x10^7 sec
divided by 2 jets= 1.18x10^7 seconds

I used N for the angular velocity because I couldn't figure out a way to get it from the velocity given since I didn't know the mass yet. Maybe that is why I can't get it right? Thanks for any help!

 

[Astronuc]

Here are descriptions of variables and equations for rotational motion, and their corresponding linear motion ones.

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

Knowing "13.7 g/s of gas with a nozzle speed of v = 712 m/s" gives a force and applied at R gives a torque.

Having I and $\omega_0$, one wants to know the deceleration and use the appropriate equation of motion to determine the time required to stop the rotation.

 

[D H]

(3872*3.56rad/s)/(.0137*3.11)= 3.24x10^5 kg

The quantity on the right-hand side does not have units of mass. When you get a goofy answer it often helps to write down all of the units. In this case,

3872 kg-m²*3.56 r/s / (0.137 kg/s * 3.11 m) = 3.24x10⁵ meters, not kilograms.

 

[Anony-mouse]

Okay, I'm confused here.
Torque=ma*l=I(alpha)
So... Torque=(0.0137 kg/s)(712 m/s)(3.11 m)=30.34 Nm
(alpha) = Torque/I = 30.34N*m / 3872 kg*m^2 = 0.00783 rad/s^2 is the angular acceleration

so (omega)=(intial omega)-(alpha)T
because it reaches a stop, (omega)=0, and initial omega is 3.56 rad/s.
so (-3.56 rad/s) / (-0.00783 rad/s^2) = 454 s

Where did I go wrong?

 

[D H]

There are two jets.