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DYNAMICS - CASE STUDY

    Introduction


Problem Diagram

 

A communications satellite is struck by a meteoroid and sent spinning. Half a second later, the satellite's thrusters fire opposite the rotation to stop the spinning.

What is known:

  • meteoroid momentum pm = 0.33 kg-km/s
  • impact angle α = 45°
  • satellite mass ms = 100 kg
  • satellite moment of inertia Is = 150 kg-m2
  • thruster force F = 200 N each
  • initial angular velocity is zero before impact
     
    Question


Problem Graphic
 

How long must the thrusters fire in order to stop the satellite from spinning?

   
  Approach

 
  • Assume the meteoroid becomes imbedded in the satellite.
  • Using the Conservation of Momentum, determine the motion of the satellite after the impact.
  • Using the Principle of Impulse and Momentum, determine the thruster firing-time required to reduce the rotational velocity back to zero.
     
   
 
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