Topic 6: Momentum, Impulse, and Collisions

Vocabulary practice flashcards covering fundamental definitions, theorems, types of collisions, and mathematical formulations for Topic 6: Momentum, Impulse, and Collisions.

Linear Momentum ($\vec{p}$)

The vector quantity defined as the product of an object's mass and its velocity ($\vec{p} = m\bar{v}$), possessing the same direction as the velocity and measured in units of $kg \cdot m/s$.

Impulse ($\vec{I}$)

The vector quantity equal to the product of a force and the time interval over which it acts ($\vec{I} = \vec{F}_{av}\Delta t$), pointing in the same direction as the force and measured in $N \cdot s$ or $kg \cdot m/s$.

Impulse-Momentum Theorem

A theorem stating that the impulse delivered to an object equals the change in momentum of that object ($\vec{I} = \vec{F}\Delta t = \Delta \vec{p} = m\vec{v}_f - m\vec{v}_i$).

Area Under the Force versus Time Graph

The geometric area between the curve and the time axis on a force-time plot, which quantitatively represents the impulse delivered by the force during the time interval $\Delta t$.

Average Force in Impulse

The constant force that produces the exact same impulse over a specific time interval as the actual time-varying force acting over that interval.

Principle of Conservation of Momentum

The principle stating that when no net external force acts on an isolated system, the total momentum of the system remains constant over time ($m_1\vec{v}_{1i} + m_2\vec{v}_{2i} = m_1\vec{v}_{1f} + m_2\vec{v}_{2f}$).

Isolated System

A physical system subject to no net external forces, meaning the vector sum of all momentum components remains constant before and after interactions.

Inelastic Collision

A collision in which the total momentum of the system is conserved, but total kinetic energy is not conserved because some energy is converted to heat, sound, or work that deforms the objects.

Perfectly Inelastic Collision

A collision in which the colliding objects stick together upon impact and move together with a single common final velocity.

Elastic Collision

A collision in which both the total linear momentum and the total kinetic energy of the isolated system are completely conserved.

Relative Velocity Equation for Elastic Collisions

A linear relation derived from conservation of momentum and energy for a one-dimensional elastic collision, given by $v_{1i} - v_{2i} = -(v_{1f} - v_{2f})$.

Ballistic Pendulum

A device used to measure the speed of a fast-moving projectile by allowing it to embed into a suspended wooden block, causing the block-bullet system to swing upward to a measurable vertical height $h$.

Impulse Approximation

The approximation in which external forces like friction are neglected during an impact because the collision occurs over an extremely brief time interval, allowing the colliding bodies to be treated as an isolated system.

Glancing Collision

A two-dimensional collision where conservation of momentum is resolved independently along two mutually perpendicular axes (the $x$-axis and $y$-axis).

Momentum-Kinetic Energy Relationship

The mathematical formula connecting an object's kinetic energy to the magnitude of its momentum: $KE = \frac{p^2}{2m}$.

Newton's Second Law in Terms of Momentum

The generalized statement of Newton's second law asserting that the constant net force acting on an object equals the rate of change of its momentum over time: $\vec{F}_{net} = \frac{\Delta \vec{p}}{\Delta t}$.