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phys: momentum and impulse intro

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eggy 2020-10-20 18:32:07 -04:00
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@ -402,6 +402,30 @@ Newton's second law of motion states that the force on an object is equal to its
## 2.4 - Momentum and impulse
### Momentum
The momentum of an object describes the difficulty of changing its motion. It is expressed mathematically as $\vec{P}$, and is equal to mass times initial velocity, or:
$$\vec{P} = m\vec{v}$$
### Impulse
Impulse is the average net force $\Sigma F_{\text{avg}}$ applied over a time interval $\Delta t$. It is expressed mathematically as $\vec{J}$, and is represented in **Newton seconds** ($\text{Ns}$). It is equal to:
$$\vec{J} = \Sigma \vec{F}_\text{avg} · \Delta t$$
This can be rearranged and combined with other formulas, if the mass of the object is **constant**, so that impulse is equal to the difference in linear momentum.
$$
\vec{J} = m\vec{a_\text{avg}} · \Delta t \\
\vec{J} = mt (\frac{\vec{v_2} - \vec{v_1}}{\Delta t}) \\
\vec{J} = m\vec{v_2} - m\vec{v_1} \\
\vec{J} = \vec{P}_2 - \vec{P}_1 \\
\vec{J} = \Delta \vec{P}
$$
Using the above, the net average force on an object can also be written as the rate of change of its momentum with respect to time.
$$
\Sigma \vec{F}_\text{avg} = \frac{\Delta \vec{P}}{\Delta t}
$$
## 3.1 - Thermal concepts
## 3.2 - Modelling a gas