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

SF = m a       (translational acceleration)

SM_CM = I_CM a   (rotational acceleration)

 

where M_CM is the moment about the Center of Mass, I_CM 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)

SM_a = 0   (rotational equilibrium)

 

where M_a is the moment about any point.