Newton's third law states that every action has an equal and opposite reaction. Consider a swimmer pushing off the side of a pool. They push against the wall of the pool with their feet and accelerate in the direction opposite to that of their push. This occurs because the wall exerts an equal and opposite force on the swimmer. Here, the forces do not cancel out each other as they are acting on different systems. In this case, there are two systems: the swimmer and the wall. If we select the swimmer to be the system of interest, the force of the wall on the feet is an external force on this system and affects its motion. Therefore, the swimmer moves in the direction of this force. In contrast, the force of the feet on the wall acts on the wall, not on our system of interest. Thus, the force of the feet on the wall does not directly affect the motion of the system and does not cancel out the force of the wall on the feet. The swimmer pushes in the opposite direction that they wish to move. The reaction to the push is thus in the desired direction.

Other examples of Newton's third law are:

• A professor pacing in front of a whiteboard exerts a force backward on the floor. The floor exerts a reaction force forward on the professor that causes them to accelerate forward.
• When a person pulls down on a vertical rope, the rope pulls up on the person.
• Helicopters create lift by pushing air down, experiencing an upward reaction force.

This text is adapted from Openstax, University Physics Volume 1, Section 5.5: Newton's Third Law.