Newton's 2nd law


Newton's three laws of motion revolutionized our view of motion and set the stage for our modern scientific thought which has led to our modern world.

But at first look, these laws seem to run against our common-sense view of the world. So let's delve into the second law and see how logical it in fact is.


A change of pace

Motion, we all do it.

But how do we describe it?


Of course, we need to talk about how fast, or the speed, of the thing we are talking about.

So when we talk about driving at 45 miles per hour, or walking at 3 miles per hour we are talking speed – how much distance we can cover every hour.


But this is not enough. We also need to include information about which way we are going (north, south, left, right, etc.)

This is where velocity comes in. Velocity is the combination of speed and direction.


For example, one can say that someone is running at 10 miles per hour. This tells you a rate; the person travels 10 miles for every hour of running (assuming they run that long). But it's not the full picture, is it? You can't completely see it.


But now say the person is running north at 10 miles per hour. Now it's more meaningful. This tells us that if the runner keeps it up for an hour he/she would change position by moving north 10 miles. We can imagine that.


Velocity gives a more complete picture.


There are A LOT of rates in science. Speed and velocity are just two. However, we also want to describe how motion changes over time. This brings us to another useful rate – useful for us at least – is called acceleration.


When people usually talk about acceleration, what is meant is speeding up.

Actually and properly, acceleration means the changing of motion (velocity) of any kind. This powerful redefinition opens up the doors to many more cases where there is an acceleration.


Acceleration covers a large territory. But what causes acceleration? What causes the motion of an object to change?


Not just a good idea, it's the law

The topic of the day is Newton's 2nd law. This implies that there must be the 1st law, no?


Indeed there is. In Newton's own words:

"An object at rest stays at rest and an object in motion stays in motion with the same speed and the same direction unless acted upon by an unbalanced force."


Another, briefer way to say this is that motion (velocity) remains unchanged unless a force changes it.


Still briefer is this; force causes a change in motion.


This is important!


Force (push, pull shove, and so on) does not cause motion.


Force makes motion change. This is why a spaceship, far away from the gravity force of anything, moves through space nonstop and in a straight-line path.


In other words, it is a force that causes acceleration. And the greater the force that pushes on an object, the greater the acceleration.


Resistance is somewhat futile

Imagine you are watching a baseball game and the batter up hits a home run.


The crowd goes crazy and it's an exciting moment. But suppose this same hitter instead hit, not a tiny baseball, but an oil tanker in the exact same way.

It doesn't take a lot of imagination to know that the tanker would not move nearly as much as the tiny baseball.


Why? We might rightly say that there is a lot more tanker to move than the small baseball. The fact is, all objects resist a force accelerating it to one level or another. This resistance is called mass or inertia.


A baseball has very little mass, it doesn't take much force to change its motion (good news for the baseball player). The tanker has a whole lot of mass (bad news for anyone trying to push it), it requires a huge engine to push it up to speed.


More mass means more force is needed to have the same change in motion.


Newton's 2nd law – the math

Putting all this together is Newton's 2nd law. Let's recap the ideas involved:


This gives us the math equation for Newton's 2nd law.


A simple, yet powerful equation.


Being balanced

Of course, there is just one final, but important, point to be made here. Simply having a force does not make an acceleration. Take the example of a tug of war.

If both sides pull with the same force, the rope remains in the same place. No change in motion.


The key is that Newton's 2nd law deals with the combination of all forces. If the forces balance each other (such as a dog tug of war) then the combined force is nothing. No acceleration.


The balancing of forces plays an important role in all our lives. Engineers designing structures, building, bridges, and so on, to study all the forces on each piece to see if it can hold up when put to the test.

Newton's 2nd law is most useful. In fact, it all but takes over the job of the 1st law. With it, we can understand how things move and be able to design useful widgets for our everyday world.


Good job Newton!


Great books

Principia

Sir Isaac Newton's masterpiece book where he goes over his theories of gravity and motion. Maybe a bit heavy of a read.


On the web

STEMonstrations: Newtons 2nd Law of Motion

An astronaut in space demonstrates Newton's 2nd law with different objects of different mass. Very fun!


Newton's Second Law

This website is part of the Physics Classroom. Not only does it go over Newton's 2nd law, but it provides some simple practice questions.


They Might Be Giants - Speed and Velocity

Video showing the difference between speed and velocity, done as a type of music video.


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