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# Impulse Units

We can determine the form of impulse units by looking at the impulse-momentum theorem, commonly written as

$$\color{black}{\Sigma \vec{F} \Delta t = \Delta m \vec{v}.}$$

If we look at the left hand side of the equation, we can see that force is multiplied by a change in time to determine the impulse.  In the SI system, this means that the unit for impulse is simply N s, or newton seconds.

Remember that a newton is a compound unit, consisting of mass and acceleration units (from Newton’s Second Law)…

$$\color{black}{ \text{N} = \text{kg} \frac{\text{m}}{\text{s}^2}.}$$

When we multiply this by seconds, there is a cancellation that occurs,

$$\color{black}{\text{N s} = \text{kg} \frac{\text{m}}{\text{s}^2} \cdot \text{s} = \text{kg} \frac{\text{m}}{\text{s}}}$$

Notice that this is simply kg m/s, which is the unit combination we use for momentum.  This shouldn’t be too surprising, since the right hand side is the change in momentum.  Remember, both sides of the equation need to have the same dimension, even if the expression of the dimension is in different units.