# What is Newton’s Second Law of Motion?

## Newton’s Second Law of Motion

In 1687, Isaac Newton published his, “Mathematical Principles of Natural Philosophy,” where he discusses, in detail, his three laws of motion. He used these laws to explore the motion of several material objects and systems.

Hey, everyone! Welcome to this Mometrix video over Newton’s Second Law of Motion. If you haven’t already, be sure to check out our video on Newton’s First Law.

Newton’s Second law of motion describes how an object’s velocity changes only when it’s acted on by an external force.

This means that a body’s rate of change in momentum is DIRECTLY proportional to the force that is applied to the body. This change in momentum happens in the direction of the applied force.

Let’s take a look at this in equation form:

**F(net) = m x a**

**F** is the net force that is applied, **m** is the mass of the object, and **a** is the object’s **acceleration**. Therefore, the net force that is imposed on the object creates a proportional acceleration. And, remember, if the net force on the object is zero, then the momentum of the object is constant and unchanging. We learned that from Newton’s First law.

Now, let’s look at our ball again, and apply our formula to see what we find.

Let’s say you apply the exact same force to two different balls. You have a yellow ball and a purple ball which has a greater **mass** than the yellow ball. When you apply the same force to them, which one do you think will fly further, and faster?

Well, we can just plug some numbers into our formula.

So, if our force is 10N, and our mass is 5kg for the yellow ball, then our acceleration ls 2 m/s/s (a=2 m/s²).

Let’s do the same thing with our purples ball. The force is 10N, the mass is 6kg, so then the acceleration is 1.667 m/s/s (a=1.667 m/s²).

Working with a real life example and using our formula to solve for the missing variable helps us to see the relationship between mass, acceleration, and force.