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DYNAMICS - CASE STUDY

    Introduction


Problem Diagram


Satellite in Deployed Position


Satellite in Stored Position

 

To accurately control the new satellite, small rocket thrusters will be used to rotate and move the satellite when in orbit. In order to know how long to fire the thrusters, the mass and moment of inertia must be known.

Due to the intricate shape of the satellite, you can't accurately calculate the moment of inertia. Your boss tells you to use the spin table to determine the moment of inertia experimentally.

What is known:

  • The change in angular displacement Δθ is 4.459 rad.
  • The change in angular velocity Δω is 1.784 rad/s
  • The spin table generates a constant 100 N m torque during the length of the test.
  • The time length of the test was not monitored.
   
  Question

 

What is the moment of inertia about the longitudinal axis Iz in the deployed configuration?

   
  Approach

 
  • The acceleration is not known, and thus M = Iα can not be used directly.
  • Use the Principle of Work and Energy for rotating rigid bodies:

    Work = Change in Kinetic Energy

    or simply,

    T1 + ΣU1-2 = T2
     
   
 
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