Chapter 9 – Linear Momentum and Collisions

Vocabulary flashcards covering linear momentum, impulse, conservation laws, collision types, center of mass, and rocket propulsion from Chapter 9.

Linear Momentum ($p$)

A vector quantity with the SI unit $kg\times m/s$, defined as $p = m \times v$, and governed by Newton's second law as $F_{\text{net}} = \frac{dp}{dt}$.

Impulse ($J$)

A quantity defined as $J = F \times \Delta t = \Delta p$, which represents the change in linear momentum imparted by a force over an elapsed time.

Impulse-Momentum Theorem

A theorem stating that the impulse applied to an object or system is equal to its resulting change in momentum ($J = \Delta p$).

Average Force ($F_{\text{avg}}$)

The average force exerted during an interaction, defined by the formula $F_{\text{avg}} = \frac{\Delta p}{\Delta t}$.

Conservation of Momentum

The principle stating that in a closed system with no net external force, the total momentum is conserved because internal forces cancel out, applicable across atomic to astronomical scales.

Elastic Collisions

Collisions in which both total momentum and total kinetic energy are conserved.

Inelastic Collisions

Collisions in which total momentum is conserved, but total kinetic energy is not conserved.

Perfectly Inelastic Collisions

Collisions in which the colliding objects stick together after impact, resulting in the maximum loss of kinetic energy while conserving momentum.

Explosions

Events in which objects separate, where total momentum is conserved and total kinetic energy increases.

Collisions in Multiple Dimensions

Collisional events where momentum is conserved independently along each coordinate direction ($x$ and $y$), analyzed via vector components with final velocities frequently calculated using the Pythagorean theorem.

Center of Mass (COM)

The mean position of mass in a system, defined as $r_{\text{cm}} = \frac{\sum m_i \times r_i}{\sum m_i}$ (or via integrals for continuous bodies), with motion governed by $M \times a_{\text{cm}} = F_{\text{ext}}$.

Tsiolkovsky Rocket Equation

The equation describing rocket propulsion as mass changes due to fuel ejection: $\Delta v = v_{\text{exhaust}} \times \ln\left(\frac{m_{\text{initial}}}{m_{\text{final}}}\right)$.

Tsiolkovsky Rocket Equation in Gravity

The propulsion equation for a rocket operating within a gravitational field: $\Delta v = v_{\text{exhaust}} \times \ln\left(\frac{m_{\text{initial}}}{m_{\text{final}}}\right) - g \times t_{\text{burn}}$.

Internal Forces

Forces exerted between objects within a defined system that cancel out in pairs and do not affect the total momentum of the system.

External Forces

Forces acting on a system from outside its boundaries, such as air resistance and friction, which can change the system's total momentum.