Conservation of Momentum Equations

Reference from the original Physics I textbook.

Conservation of Momentum Equations

When the net external impulse on the system is zero: Σp⃗_i = Σp⃗_f.

For a 2-Body Problem: ${\vec{p}}_{1, i} + {\vec{p}}_{2, i} = {\vec{p}}_{1, f} + {\vec{p}}_{2, f}$

2-Body Problem, Expanded: $m_{1} {\vec{v}}_{1, i} + m_{2} {\vec{v}}_{2, i} = m_{1} {\vec{v}}_{1, f} + m_{2} {\vec{v}}_{2, f}$

If 1 body is initially at rest: $m_{1} {\vec{v}}_{1, i} = m_{1} {\vec{v}}_{1, f} + m_{2} {\vec{v}}_{2, f}$

Completely Inelastic Collision with body at rest: $m_{1} {\vec{v}}_{1, i} = (m_{1} + m_{2}) {\vec{V}}_{f}$

Above Situation, solved for ${\vec{V}}_{f}$ : ${\vec{V}}_{f} = \frac{m_{1}}{m_{1} + m_{2}} {\vec{v}}_{1, i}$

${\vec{p}}_{n} = Momentum of body n (N \cdot s)$
$m_{n} = Mass of body n (kg)$
${\vec{v}}_{n, i} = Initial velocity of body n (m/s)$
${\vec{v}}_{n, f} = Final velocity of body n (m/s)$
${\vec{V}}_{f} = Final velocity of two stuck bodies (m/s)$

$[\begin{aligned} 1 Newton & = 1 kg \cdot m / s^{2} \end{aligned}]$

Related Glossary Terms

Collision Equations, Momentum Equation

Index

Chapter 4 - Introduction to Momentum

Chapter 4 - Inelastic Collisions

Chapter 4 - Elastic Collisions

Chapter 4 - FFR - Kinetic Energy

Chapter 5 - Kinetic Energy

Reviewed physics notes (1)

These corrections keep the original lesson’s purpose while fixing errors in the source edition.

Momentum conservation requires negligible net external impulse. — Reference 1

About this edition and its source ↗

Glossary and deeper reading · 1 refreshers

These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.

Linear momentum
Linear momentum is a vector describing an object’s motion and equals mass times velocity in the nonrelativistic model. The vector sum of momenta is conserved when the net external impulse on the system is zero. For example, two identical carts moving equally fast in opposite directions have zero total linear momentum but nonzero total kinetic energy.
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Conservation of Momentum Equations

Linear momentum

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