Newton’s Second Law

Newton’s Second Law is the backbone of kinematics.  The key point about this equation that you need to remember is that it is a vector equation.  The vector sum of all forces is equal to the mass times the acceleration vector.   In English, that sounds more complicated than the usual:  “The net force is equal to the mass times the acceleration.”

Write Newton’s Second Law as a Vector Equation

Mathematically, we should write

\(\color{black}{ \vec{F} = m \vec{a} }\)

rather than

\(\color{black}{ F = m a.}\)

Here’s a quick video explaining this in more detail.


The key point to remember is that the object can only accelerate in one direction, even though multiple forces can act.  Combine the forces into two perpendicular components, then apply Newton’s Second Law to each of these components.

\(\color{black}{ \vec{F}_{net_x} = m \vec{a}_x \textrm{  and  } \vec{F}_{net_y} = m \vec{a}_y}\)

Many times, one of the two components will have a net force of zero, resulting in no acceleration along that direction.

youtube link:

If you have any questions about Newton’s Second Law, please ask them in the reply section below.