Translational Motion & its Forces

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.

(Eq 1)  $F_x=ma_x$

(Eq 2)  $F_y=ma_y$

(Eq 3) $F_z=ma_z$

(Eq 4) $F_n=ma_n$

(Eq 5)  $F_t=ma_t$

(Eq 6)  $∑M=0$

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

Leave a Reply