Translation

Recall, translation means every straight line in the body remains parallel to its initial position during the motion. This implies that there is no angular motion, i.e. = = 0.

Therefore, the equation of motion simplify to

Notice that translation can only occur when the resultant of the external forces acting on the body has its line of action through the mass center G of the body. Therefore, the summation of moments for a translating body will be zero only when summed about G!

If needed, we can also use the kinematic relationships for fixed axis rotation.

The solution of translation problems often involves both the equations of motion and the kinematic relationships.