71 Overcoming Inertia

Typically an RN like Jolene will walk several miles over the course of a 12 hour shift on the MED floor. Her average speed (v_{ave}) can be calculated as the distance covered divided by the time she worked. If she walks three miles, then her average speed would be:

(1)   \begin{equation*} v_{ave} = \frac{distance}{time\, interval} = \frac{3 \, miles}{12 \, hours} = 0.25 \,\bold{mph} \end{equation*}

Jolene’s average speed is very different from her instantaneous speed at any one moment in time, which could be anything from zero to about 4.5 mph (she tries to avoid running in the hospital). Jolene’s instantaneous speed and direction of motion change often as she starts, stops and turns corners. The process of generating, maintaining, and changing motion is known as locomotion.

Newton’s Third Law of Motion

Newton's First Law tells us that Jolene must experience a net force in order to initiate a change in motion, also known as a change in velocity. We know that Newton's Second Law tells us how to calculate the net force Jolene needs in order to achieve a particular amount of velocity change each second (id=”4053″]acceleration[/pb_glossary]). However,  Jolene can’t apply a net force to herself, so how exactly does Jolene control how much net force she experiences? Newton's Third Law provides the answer. The forces that Jolene experiences must be supplied by the objects around her. The size of the force that Jolene receives from another object, such as the floor or wall, is determined by how hard she pushes against that object. In fact, anytime one object puts a force on a second object, the first object will receive an equal force back, but in the opposite direction. This result is known as Newton's Third Law of Motion. The capacity for using the laws of motion to generate, maintain, and change motion is known as locomotion.



The astronaut in the video above starts out in static equilibrium relative to the space station. Then she pushed against the wall. The resistance of the wall to being deformed caused it to apply a reactionary normal force back on her. That unbalanced normal force destroyed her state of static equilibrium, overcame her inertia, and caused her velocity to change relative to the station. This example is a unique form of locomotion, but all locomotion depends on this same process of pushing on an object in order receive a push back form the object (even if that object is air or hot exhaust gas from a rocket engine).

Reinforcement Activity

Third Law Pair Forces

The equal and opposite forces referenced in Newton’s Third Law are known as third law pair forces (or third law pairs).

Other Third Law pair forces include:

  • The Earth pulls down on you due to gravity and you pull back up on the Earth due to gravity.
  • A falling body pushing air out of its way and air resistance pushing back on the body.
  • You pull on a rope and the rope pulls back against your hand via tension.
  • You push on the wall, and the wall pushes back with a normal force.
  • A rocket engine pushes hot gasses out the back, and the gasses push back on the rocket in the forward direction.
  • You push your hand along the wall surface, and the wall pushes back on your hand due to kinetic friction.
  • You push your foot against the ground as you walk, and the floor pushes back against your food due to friction (static if your foot doesn’t slip, kinetic if it does).

You may have noticed that in each of the cases above there were two objects listed. This is because Newton’s Third Law pairs must act on different objects.  Therefore, Third Law pair forces cannot be drawn on the same free body diagram and can never cancel each other out.  (Imagine if they did act on the same object, then they would always balance each other out and no object could ever have a net force, so no object could ever accelerate!)

Reinforcement Exercises

Draw the free body diagrams necessary to show each force in the Third Law pairs listed above. How many free body diagrams will you need to draw for each Third Law pair? [Hint: keep in mind the rule about free body diagrams and Third Law pairs.]

Reinforcement Exercises

Everyday Example: Headrest

The headrest in your car is not actually designed as a place to rest your head. Its real purpose is to prevent injury. If someone rear-ends your car it will accelerate forward. As a result your body is accelerated forward by normal force and friction from the seat. If the head rest were not there, your head would momentarily remain in place due to inertia as your body moved forward. The lag in head position gives the impression that the head snapped back, but really the body moved forward and left the head behind. Your head does remain attached to your accelerating body though, so the tissues in your neck must provide the large force required to accelerate the head along with the body. According to Newton’s Third Law, the tissues of the neck will feel an equal and opposite force to that large force they apply to the head. That large force may damage the tissue (cause a stress larger than the yield stress of the tissue).

First image: The spine in a near vertical position while the head is moving from an extreme rearward position forward to a face-down position. Force pairs of equal length and opposite direction shown the force of the neck on the head and head back on the neck. Second and third images: Regions of injury on the front of the neck (soft tissue) and back of the neck (soft tissue and spine) are highlighted.
Top: Forces on the head from the neck (black) and on the neck from the head (red) during rapid forward-back motion of the head relative to the body. Bottom: Sites of whiplash injury. Image Credit: 3rd Law Whiplash is a derivative of Whiplash Injury by BruceBlaus, via Wikimedia Commons


The headrest provides a normal force on your head so that it accelerates along with the body, keeping your head above your shoulders and your neck in a safe position. You can see the importance of the headrest in these crash-test videos:

The headrest doesn’t necessarily reduce the acceleration felt by the head as much as provide the force needed to accelerate the head along with the body, so that the neck doesn’t have to, thus reducing the third law pair forces between the head and neck.

Falling as Locomotion

Notice that the list of third-law pair forces includes the force of gravity on the Earth from you and the force of gravity on you from the Earth (weight), so in fact falling is a form of locomotion. That means that throughout the previous unit on falling we were already studying locomotion, although falling is sort of an uncontrolled, or passive form of locomotion. The next few chapters will help us examine active forms of locomotion like walking, jumping and driving.


  1. 3rd Law Whiplash is a derivative of Whiplash Injury by BruceBlaus [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons


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