Another version of Newton’s 2nd Law

In the textbook, we have Newton’s second law listed as:

\vec{F}_\text{net} = m\vec{a}

However, if you look at some of my older videos, you will that I write:

\vec{F}_\text{net} = \frac{\Delta \vec{p}}{\Delta t}

In fact, these are mostly the same equation.  What is this “p”?  That is the momentum (which we haven’t looked at yet, but we will).  For most cases in this course, the momentum can be defined as:

\vec{p} = m\vec{v}

In the case of an object with a constant mass, I can say that the change in momentum divided by the change in time is:

\frac{\Delta \vec{p}}{\Delta t} = \frac{\Delta(m\vec{v})}{\Delta t} = m\frac{\Delta \vec{v}}{\Delta t} = m\vec{a}

So, the same thing.

If these are the same, why would anyone do it in terms of the momentum instead of the acceleration?  It turns out that using momentum is more general and works in more cases.  Let’s just leave it at that.

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