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Sum of Moments Derivation

Extra Credit (2pts)

The dynamics equations of motion for rigid body motion is a plane is given by:

SF = m a       (translational acceleration)

SMCM = ICM a   (rotational acceleration)


where MCM is the moment about the Center of Mass, ICM is moment of inertia about the Center of Mass, and a is the angular acceleration.


Prove that for static or quasi-static analysis, the sum of moments can be taken about any point, as shown below


SF = 0       (translational equilibrium)

SMa = 0   (rotational equilibrium)


where Ma is the moment about any point.