Angular Momentum difficult problem

[Arshad_Physic]

1. The problem statement, all variables and given/known data

The rear view of a space capsule that is rotating about its longitudinal axis is 3rev/min. The occupants want to stop this rotation. They have small jets mounted tangentially at a distance 1.2 m from the axis, as indicated, and can eject 8 g/s of gas from each jet with a nozzle velocity of 591 m/s. The moment of inertia of the ship about its axis (assumed to be constant is 2200 kg m2.

2. Relevant equations

This is the final equation my professor gave: t= [L (initial)]/ ((m/t)*R*V)^2

Also, L(initial) = Iw


3. The attempt at a solution

Hello. My computer generated homework gave 10 questions. I was able to solve 9 of them, but this one seems IMPOSSIBLE! lol :) I know that this has been solved in Physics forums in April 2007, but it doesn't makes sense to me :(

I tried to understand what professor told me as to HOW to solve this problem. But I just didn't get it. Even worse, I tried plugging in the answer and I didn't get it right lol.


I know that

w = 3rev/s * 2pi * 1/60 = pi/10 rad/sec

L(initial) is Iw = 2200*

m/t = 8g/s = 0.008 kg/s

R=1.2m

V = 591 m/s

But when I plug in the equations I just get the WRONG answer :(

I THINK that the problem is with the part that I plug in 0.008 kg/s for the part in the equation where I am supposed to plug in m/t.

Please helP!!!

Thanks! :)

Arshad

[Delphi51]

t= [L (initial)]/ ((m/t)*R*V)^2
The dimensions don't seem to work out in this formula!
Using the linear/rotational analogy, if you start with the impulse formula
Ft = p
τt = L
t = L/τ = L/(m/t*R*v)
you get the same formula but without the square.

[Arshad_Physic]

I get answer t = 122 secs using the equation you give, which is wrong. The equation my professor gave is wrong too, for I get answet t = about 21 seconds.

I got some help, and I got the right answer. We first find Torque. Divide the torque by Inertia to get angular acceleration. Using that we plug it into the equation 0=wi+0.5At^2, where A = angular acceleration.

My answer turned out to be t = 60.something and the program thingy accepted it! :)

THanks for your help though, very much! :)

[Delphi51]

Thanks for the report! Always nice to see how it turns out. But I'm puzzled because "0=wi+0.5At^2" is not a valid formula - should be 0 = wi+αt, which should give the same answer as our
t = L/τ = L/(m/t*R*v)
You don't say how many rockets there are, but if there are 2, we get
t = I*ω/(m/t*R*v)
= 2200*3(2π)/60 all divided by (2*.008*1.2*591)
= 60.9 seconds.