eqn – Aerospace Insights

Definition of momentum\\

It is convenient to define a physical quantity called momentum, usually indicated by the symbol $p$ , as the product of its mass $m$ by its velocity $\vec{v}$

(1) $\begin{equation*} \vec{p} = m \vec{v} \end{equation*}$

The momentum is a vector quantity which has the same direction as the velocity of a body.

The unit of measurement of momentum in the SI system is the product of the units of mass and velocity and thus is the kg m/s.

A new form of the Second Newton’s Law\

Newton’s Second Law can be expressed in terms of change in momentum:

(2) $\begin{equation*} \vec{F}{net} = m \vec{a} = m \frac{(\vec{v}{final} -\vec{v}{initial} )}{\Delta t} = \frac{m \vec{v}{final} - m \vec{v}{initial} }{\Delta t} = \frac{\vec{p}{final} -\vec{p}{initial} )}{\Delta t} \end{equation*}$

which can be written in the more compact form

(3) $\begin{equation*} \vec{F}{net} = \frac{\Delta \vec{p}}{\Delta t} \end{equation*}$