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DYNAMICS - CASE STUDY

    Introduction


Problem Graphic
 

People riding the spinning-disk ride at Fun Time, Inc. are complaining about high accelerations. An investigation found that the maximum acceleration was occurring at 2.4 seconds.

What is known:

  • The main disk rotates at Ω = 1 rad/s (θ = Ωt).
  • The rider disk rotates at ω = 2 rad/s (β = ωt).
  • Both angular velocities are constant.
  • Both disks have no angular acceleration (dω/dt = 0, dΩ/dt = 0).
     

  Question

 

What is the acceleration of the rider at 2.4 seconds and is it unsafe?

   
  Approach

 
  • Use the relative acceleration equation for rotating coordinates,

    aB = aA + dΩ/dt × rB/A + Ω × (Ω × rB/A
                + 2 Ω × vB/A + aB/A
     
   
 
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