Linear Momentum and Center of Mass 07

Practice flashcards covering linear momentum, impulse, collision types, and center of mass concepts from Chapter 07.

Linear Momentum

A vector property of moving objects defined as the product of mass and velocity: $\mathbf{p} = m\mathbf{v}$, measured in $\text{kg} \cdot \text{m/s}$.

Newton’s Second Law (Force-Momentum relation)

States that the net external force on an object is equal to the rate of change of its momentum: $\mathbf{F}_{net} = \frac{\Delta \mathbf{p}}{\Delta t}$.

Impulse ($\mathbf{J}$)

A force applied on an object over a time interval that causes a change in momentum, defined as $\mathbf{J} = \Delta \mathbf{p} = \mathbf{F} \cdot \Delta t = m\Delta\mathbf{v}$.

Conservation of Linear Momentum

A principle stating that the total momentum of an isolated system remains constant ($\Delta \mathbf{p} = 0$) if the net external force is zero ($\mathbf{F} = 0$).

Elastic Collision

A collision where the total momentum and total kinetic energy are conserved ($\text{KE}_{initial} = \text{KE}_{final}$), with no energy lost to heat.

Inelastic Collision

A collision where momentum is conserved ($\mathbf{p}_{initial} = \mathbf{p}_{final}$) but some kinetic energy is lost to heat; often, the masses move at the same velocity after the collision.

Coefficient of Restitution ($\epsilon$)

A ratio defined as $\epsilon = \frac{\mathbf{v}_2 - \mathbf{v}_1}{\mathbf{u}_2 - \mathbf{u}_1}$, where $\epsilon = 1$ for elastic collisions and $\epsilon = 0$ for inelastic collisions.

Center of Mass ($x_{cm}$)

A unique point used to describe a system's response to external forces, calculated as $x_{cm} = \frac{\sum m_i x_i}{\sum m_i}$, reflecting how the system moves as if it were a point particle.

Center of Gravity

The point where the force of gravity can be considered to act; for small masses, this is the same location as the center of mass.

Net Force of a System (Translational Motion)

The relationship stating that the net force on a system is equal to the total mass multiplied by the acceleration of the center of mass: $\mathbf{F}_{net} = m_{total}\mathbf{a}_{cm}$.

Kinetic Energy ($KE$) in Terms of Momentum

The formula relating kinetic energy to momentum and mass: $KE = \frac{p^2}{2m}$.