| − | Force is defined as dp/dt, or (change in momentum) / (change in time). Say, over a period of time, the force imparts a momentum p to the moving object. Since momentum in the perpendicular direction is initially 0, its final momentum in the perpendicular direction will be p. <math>p=\gamma_y*m*v_y</math>. If the new momentum is small, <math>\gamma_y=0</math> (the gamma factor in the perpendicular direction), <math>v_y</math> = perpendicular velocity and m = rest mass. Thus the force will act on the rest mass. | + | Force is defined as dp/dt, or (change in momentum) / (change in time). Say, over a period of time, the force imparts a momentum p to the moving object. Since momentum in the perpendicular direction is initially 0, its final momentum in the perpendicular direction will be p. <math>p=\gamma_ymv_y</math>. If the new momentum is small, <math>\gamma_y=1</math> (the gamma factor in the perpendicular direction), <math>v_y</math> = perpendicular velocity and m = rest mass. Thus the force will act on the rest mass. |