The 'Sears paradox'
  We resolve a paradox in special relativity proposed by F. W. Sears for the action of forces on a rigid body. In the paradox, a moving rigid rod is struck at different times by impulsive forces, but continues to move with unchanged velocity, with the forces having no effect. Our conclusion is that the usual laws of mechanics can be applied to a rigid body only in its rest system 
Jerrold Franklin
physics.gen-ph