Summary -Important Principles (Work and Energy)

 

Integration of Euler’s first law

Σ F = m aC

Euler’s First Law

with respect to displacement yields

 

 

                  2        

∫ Σ F ● dr =  ½ m (vc2)2  -  ½ m (vc1)2

                 1    

 

 

Integration of Euler’s second law

Σ MC = ICzz α

Euler’s Second Law

with respect to displacement yields

 

 

              2        

∫ Σ MC ● dθ =  ½ ICzz (ω2)2  -  ½ ICzz (ω1)2

             1    

 

 

note:  C  refers to the center of mass of the body

                                               

W1-2  =  T2  -  T1

Principle of Work/Energy

 

             Total work done equals total change in kinetic energy of system.

 

W1-2 = the work by all forces and moments acting on the body or bodies that actually

           do work on the body or bodies from position 1 to  position 2

 T2  =  the total kinetic energy of the body or bodies in position 2

 T1  =  the total kinetic energy of the body or bodies in position 1

 

Total Work:                    2                    2

                        W1-2    =    ∫ Σ F ● dr  +  ∫ Σ MC ● dθ  =  work by forces + work by moments

                                        1                    1

 

Total Kinetic Energy:      T  =  ½ mvc2  + ½ Iczz ω2     (ft lb or N m)

 

 

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