Rotational Intertia of a rotating Space Station

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SUMMARY

The discussion centers on calculating the rotational inertia of a rotating space station subjected to a torque from four rockets. Each rocket exerts a force of 65.5 N at a distance of 11.2 m from the center, resulting in a total torque of 2934.4 N·m. Using the formula τ = Iα, the calculated rotational inertia is 808374.7 kg·m², with the correct units confirmed as kg·m². Participants clarified the importance of proper unit notation, correcting an initial misrepresentation of the units for inertia.

PREREQUISITES
  • Understanding of torque and its calculation (τ = F × d)
  • Familiarity with angular acceleration and its units (rads²)
  • Knowledge of moment of inertia and its significance in rotational dynamics
  • Basic grasp of Newton's laws of motion, particularly F = ma
NEXT STEPS
  • Study the principles of rotational dynamics and the role of torque in motion
  • Learn about the derivation and significance of moment of inertia in various systems
  • Explore the relationship between linear and angular quantities in physics
  • Investigate real-world applications of rotational inertia in engineering and space mechanics
USEFUL FOR

Students in physics, aerospace engineers, and anyone interested in the dynamics of rotating systems, particularly in the context of space exploration and satellite mechanics.

slingshotnz
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Homework Statement


Four rockets attached to a (wheel) space station exert a force of 65.5N to rotate it . The space station's angular velocity is increased at a constant acceleration of 3.63 x 10-3 rads-2. Each rocket is 11.2m away from the centre. Calculate the rotational inertia of the system.

Homework Equations



τ=Iα , others unknown.

The Attempt at a Solution


Torque of all 4 rockets. (65.5N * 11.2) * 4 = 2934.4N
since τ=Iα, I=τ/α hence I= 2934.4/3.63x10-3 = 808374.7Kgm2

Can anyone confirm if this is the correct method.

Thanks.
 
Last edited:
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The units for inertia are wrong. What are the derived units for the Newton? (Hint: F = ma)
 
Sorry Kg metres squared?. Other than that does the working look fine? I appreciate the advice.
 
Last edited:
Not sure, but I think SteamKing may be referring to this item:
slingshotnz said:
Torque of all 4 rockets. (65.5N * 11.2) * 4 = 2934.4N
force in N * distance in m gives what units?
(Your method and answer look ok.)
 
I missed the torque units. But the units for moment of inertia should be kg-m^2. OP originally had kg-m^-2.
 

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