# Newton's Second Law

In our lesson on inertia, we defined what a force is and stated Newton's first law of motion - The Law of Inertia.  Since an object requires an external force in order to change its velocity (whether moving or at rest), it would be helpful to see what effect that force has on the motion of the object.

Let's start by assuming we place a force on an object. Since our goal is to change the velocity of the object (either the speed or direction of motion or both), then we can say we are also causing the object to accelerate. This is the heart of Newton's second law of motion and it relates force to acceleration. We state this as:

The acceleration on an object is directly proportional to the net force exerted on the object and is inversely proportional to the mass of the object.

Mathematically, we write

or the more common form

Notice that both force and acceleration are vector quantities. Mass is a scalar, but the product of a vector and a scalar is a vector. Notice also that we are going to get lazy here and leave the arrows off the top of the vectors.

Newton's second law is probably the most important law in Physics (although Einstein's E=mc2 is probably the most recognizable) and we will use this a lot in our problem solving. It has some important implications. The first is not always obvious to students; if there is no acceleration on an object (i.e. at rest or moving with a constant
velocity) then the net force on the object must be zero. The second is that we can look at Newton's second law in more than just linear motion or one dimension. Net force in the x-axis will cause an acceleration in the x axis only. Net force in the y-axis will cause acceleration in the y-axis. The same is true in the z-axis.

Often it is helpful to see what someone else has to say on the topic. For more on Newton's Second Law:

http://www.physicsclassroom.com/Class/newtlaws/u2l3a.cfm

http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html

http://theory.uwinnipeg.ca/physics/force/node3.html

Walter Fendt provides some good applets to help with the understanding of the material.. Check out:

Equilibrium of 3 Forces

Resultant of Forces (Addition of Vectors)

Newton's Second Law Experiment

For Practice Problems, Try:

From the University of Oregon, Go to this page and select and appropriate problem (don't worry - you won't be able to do all of them yet): http://zebu.uoregon.edu/~probs/mech/newt.html

Giancoli Multiple Choice Practice Questions (Select "Practice Problems) and try some.