This is by far the toughest law to master. Once I help my tutoring students get past the math hurdles from the 2nd Law, we spend a lot of time working through the math and concepts of the 3rd. Let’s start in a familiar frame and then we’ll start asking tougher questions. 

Consider a person standing in an elevator. They’ve got basically two forces acting on them: the force of gravity pulling down and the force exerted upwards on them by the floor of the elevator. When I stand in a stationary elevator, how hard do I push on the floor? How hard does it push on me? If I weighed 150 lbs, then it stands to reason that I’m pushing down on the floor with as much force as I weigh. How hard, then, does the floor push back? I can use my eyes to answer this one. If I’m not moving, then the net force on me must be zero. Since I’m pushing down on the floor with 150 lbs of force, then the ground must be pushing up just as hard, with 150 lbs of force. I love this example. It’s clean and intuitive. Let’s change the conditions, though, and see if Newton’s 3rd still describes what’s going on here.

Say that I’m in an elevator that is accelerating downward, just like it does once it starts moving downward. How hard do I push on the elevator then? As the elevator accelerates downward away from me, I’ll be pushing on it less than when it was stationary, so less than the 150 lbs of my weight. Does it push on me less, then? Sure! If I’m accelerating downward, I have to have more force pulling down than pushing up. As gravity’s pull doesn’t change then the push upwards from the floor must decrease. 

Let’s try another question: if an unbalanced force is required to cause acceleration, then why does anything move if it always pushes back as hard as it’s pushed? This can be hard to intuit. Remember, though, that if I'm to accelerate I have to be pushed by an *outside force*. Imagine I push on the dashboard of my car from the driver’s seat. Now imagine I apply the same force to the trunk from outside the car. Which causes the car to roll? The second, obviously! Although both inside and outside pushes from me are countered by and equal and opposite forces from the car, only one comes from outside the car and, thus, only one rolls the car! 

This can be tough to intuit! **The key things to remember here are that Newton’s 3rd describes the interactions between objects NO MATTER how they move. Also, push your car from the outside!**

Physics and Math are hard! Ask your teacher for help if you need it. Ask me if you need more.

There is evidence for this observation everywhere: Interstellar spacecraft like the Voyager probes haven’t had any engines on for decades, yet they still move through space at more than 35,000 mph. Air hockey pucks move seemingly forever, even with a very light starting tap. Finally, stationary rocks never spontaneously start moving. In these examples, motion is maintained without any force at all.