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<h2>Newton's Third Law of Motion</h2>
<p>There is a passage in the musical <em>Man of la Mancha</em> that relates to Newton's third law of motion. Sancho, in describing a fight with his wife to Don Quixote, says, “Of course I hit her back, Your Grace, but she's a lot harder than me and you know what they say, ‘Whether the stone hits the pitcher or the pitcher hits the stone, it's going to be bad for the pitcher.‘”</p>
<p>This is exactly what happens whenever one body exerts a force on another—the first also experiences a force (equal in magnitude and opposite in direction). Numerous common experiences, such as stubbing a toe or throwing a ball, confirm this. It is precisely stated in <strong>Newton's third law of motion</strong>.</p>
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<h3 data-type="title">Newton's Third Law of Motion</h3>
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<p>Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts.</p>
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<p>This law represents a certain <em>symmetry in nature</em>: Forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself. We sometimes refer to this law loosely as “action-reaction,” where the force exerted is the action and the force experienced as a consequence is the reaction. Newton's third law has practical uses in analyzing the origin of forces and understanding which forces are external to a system.</p>
<p>We can readily see Newton's third law at work by taking a look at how people move about. Consider a swimmer pushing off from the side of a pool, as illustrated in the figure below. She pushes against the pool wall with her feet and accelerates in the direction <em>opposite</em> to that of her push. The wall has exerted an equal and opposite force back on the swimmer.</p>
<p>You might think that two equal and opposite forces would cancel, but they do not <em>because they act on different systems</em>. In this case, there are two systems that we could investigate: the swimmer or the wall. If we select the swimmer to be the system of interest, as in the figure, then \({\mathbf{\text{F}}}_{\text{wall on feet}}\) is an external force on this system and affects its motion.</p>
<p>The swimmer moves in the direction of \({\mathbf{\text{F}}}_{\text{wall on feet}}\). In contrast, the force \({\mathbf{\text{F}}}_{\text{feet on wall}}\) acts on the wall and not on our system of interest. Thus \({\mathbf{\text{F}}}_{\text{feet on wall}}\) does not directly affect the motion of the system and does not cancel \({\mathbf{\text{F}}}_{\text{wall on feet}}\). Note that the swimmer pushes in the direction opposite to that in which she wishes to move. The reaction to her push is thus in the desired direction.</p>
<div class="wp-caption alignnone" style="width: 800px"><img alt="A swimmer is exerting a force with her feet on a wall inside a swimming pool represented by an arrow labeled as vector F sub Feet on wall, pointing toward the right, and the wall is also exerting an equal force on her feet, represented by an arrow labeled as vector F sub Wall on feet, having the same length but pointing toward the left. The direction of acceleration of the swimmer is toward the left, shown by an arrow toward the left." height="301" src="https://data.ulearngo.com/assets/75e5ef5f-288e-4bfa-b253-55e178aafd08" width="800"/><p class="wp-caption-text">When the swimmer exerts a force \({\mathbf{\text{F}}}_{\text{feet on wall}}\) on the wall, she accelerates in the direction opposite to that of her push. This means the net external force on her is in the direction opposite to \({\mathbf{\text{F}}}_{\text{feet on wall}}\). This opposition occurs because, in accordance with Newton's third law of motion, the wall exerts a force \({\mathbf{\text{F}}}_{\text{wall on feet}}\) on her, equal in magnitude but in the direction opposite to the one she exerts on it. The line around the swimmer indicates the system of interest. Note that \({\mathbf{\text{F}}}_{\text{feet on wall}}\) does not act on this system (the swimmer) and, thus, does not cancel \({\mathbf{\text{F}}}_{\text{wall on feet}}\). Thus the free-body diagram shows only \({\mathbf{\text{F}}}_{\text{wall on feet}}\), \(\mathbf{\text{w}}\), the gravitational force, and \(\mathbf{\text{BF}}\), the buoyant force of the water supporting the swimmer's weight. The vertical forces \(\mathbf{\text{w}}\) and \(\mathbf{\text{BF}}\) cancel since there is no vertical motion.</p></div>
<p>Other examples of Newton's third law are easy to find. As a professor paces in front of a whiteboard, she exerts a force backward on the floor. The floor exerts a reaction force forward on the professor that causes her to accelerate forward.</p>
<p>Similarly, a car accelerates because the ground pushes forward on the drive wheels in reaction to the drive wheels pushing backward on the ground. You can see evidence of the wheels pushing backward when tires spin on a gravel road and throw rocks backward. In another example, rockets move forward by expelling gas backward at high velocity.</p>
<p>This means the rocket exerts a large backward force on the gas in the rocket combustion chamber, and the gas therefore exerts a large reaction force forward on the rocket. This reaction force is called <strong>thrust</strong>. It is a common misconception that rockets propel themselves by pushing on the ground or on the air behind them. They actually work better in a vacuum, where they can more readily expel the exhaust gases.</p>
<p>Helicopters similarly create lift by pushing air down, thereby experiencing an upward reaction force. Birds and airplanes also fly by exerting force on air in a direction opposite to that of whatever force they need. For example, the wings of a bird force air downward and backward in order to get lift and move forward.</p>
<p>An octopus propels itself in the water by ejecting water through a funnel from its body, similar to a jet ski. In a situation similar to Sancho's, professional cage fighters experience reaction forces when they punch, sometimes breaking their hand by hitting an opponent's body.</p>

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Newton's Third Law of Motion: Symmetry in Forces

Physics is a science discipline concerned with the nature and properties of matter and energy. Physics topics include mechanics, heat, light and radiation, sound, electricity, magnetism, the structure of atoms, and so on.

Physics

Discover the development of the force concept, explore Newton&#8217;s first, second, and third laws of motion, and learn about problem-solving strategies and further applications in this tutorial on dynamics and the four basic forces.


Newton's Third Law of Motion: Symmetry in Forces

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