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The units of force are relatively easy to understand, especially if you know Newton’s Second Law.

## The newton

The unit of force in the metric system is the newton.  Notice that the newton does not have a capital letter.  When we use SI units, we do not capitalize the first letter of unit terms, even if the name is derived from a proper name (as many are).  Therefore, we write things like newtons, joules, hertz, etc.  However, the common practice is to capitalize the letter representing the unit when it comes from a proper name.  Therefore, we can write ten newtons as 10 N, where N is the abbreviation for newtons.  Likewise 10 watts is written as 10 W, 10 joules is written as 10 J, etc.

## Units of Force

Newton’s Second Law states that $$\color{black}{\Sigma \vec{F} = m \vec{a}}$$.

If we look at the right hand side of this equation, we see that we are multiplying a mass by an acceleration.  We already know the units of each, so we are multiplying kg by m/s².  The other side of the equation is a force, which we just learned is given in units of newtons (N).

A newton is defined as the force required to accelerate a mass of 1 kg at 1 m/s². So we see that…

$$\color{black}{\Sigma \vec{F} = m \vec{a}}$$,

which gives us…

$$\color{black}{1 \text{N} = 1 \text{kg} \cdot 1 \frac{\text{m}}{\text{s²}}}$$
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