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DYNAMICS - THEORY


Relative Acceleration Equation

 

 

 

Relative acceleration equation can be derived from the the relative velocity equation,

     vB = vA + vB/A

Differentiate with respect to time to give

                    dvB/dt =dvA/dt + dvB/A/dt

 
aB = aA + aB/A
 

Just like the relative velocity equation, the relative acceleration equation can be separated into linear motion and angular motion. However, it is important to note that the angular motion has two components, tangential and normal acceleration.

     

     

3-Bar Acceleration Motion
 

Each rotation term can be written as cross products, giving

     aB = aA + ωAB × (ωAB × rAB) + αAB × rAB

This form shows that the relative acceleration is composed of the translating motion of base point A and the rotating motion of point B about A.

For plane motion, the normal rotation terms can be simplified as -ω2r giving

     aB = aA - ω2rAB + α × rAB

Another way to write the relative acceleration equation is

     aB = aA - ω2ren + αret

     
   
 
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