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

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SUMMARY

The discussion revolves around solving a physics problem related to stopping the rotation of a space capsule initially rotating at 30 revolutions per minute (rev/min). The flight controller must calculate the time required for two jets, each ejecting gas at 7.0 grams per second with a nozzle speed of 800 m/s, to stop the capsule's rotation. The moment of inertia of the capsule is given as 5800 kg·m². The correct calculation for the time to stop the rotation is determined to be approximately 9.04 seconds, although the initial attempt contained an error in the value of omega.

PREREQUISITES
  • Understanding of rotational dynamics, specifically torque and angular acceleration.
  • Familiarity with the equations of motion for rotational systems, including τ = Iα and αt = ω.
  • Knowledge of units conversion, particularly between grams and kilograms.
  • Basic principles of fluid dynamics as they relate to jet propulsion.
NEXT STEPS
  • Review the calculation of torque using τ = F x r in rotational dynamics.
  • Study the relationship between angular velocity (ω) and angular acceleration (α) in rotational motion.
  • Explore the effects of moment of inertia on rotational motion and how it influences stopping time.
  • Investigate the principles of jet propulsion and how thrust is generated in spacecraft systems.
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Students studying physics, aerospace engineers, flight controllers, and anyone interested in the dynamics of rotational motion and spacecraft maneuvering.

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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?
 

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

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