Recall from kinematics of a rigid body, there is no rotation if the motion of the rigid body has translational motion. This means that if a line segment is drawn between two particles, that line segment should remain parallel as that rigid body moves from point a to point b, which results in no rotational force since there is no rotation about a fixed axis. So to calculate the forces on the rigid body from certain acceleration you would only have to consider different variables of F=ma, which can be seen in the equations below. You may also need to consider moments when dealing with a rigid body. However, the moments for a rigid body will sum to zero.

Equation 1-6 represents the forces in the x, y, z, normal, and tangential directions.

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