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)

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.