AP Physics C: Mechanics
Advanced Placement Physics C: Mechanics with calculus-based physics principles.
Systems of Particles and Linear Momentum
Beyond Single Objects
Many real-world problems involve multiple interacting objects. The concept of momentum helps us analyze these complex systems.
Linear Momentum
Momentum (\( \vec{p} \)) is mass times velocity: \( \vec{p} = m\vec{v} \). It's a vector, so direction matters!
Conservation of Momentum
In the absence of external forces, the total momentum of a system is conserved: \[ \sum \vec{p}{\text{initial}} = \sum \vec{p}{\text{final}} \]
Center of Mass
Calculus lets us find the center of mass and analyze how a group of particles moves collectively.
Collisions
Elastic and inelastic collisions illustrate momentum conservation and energy transfer.
Real-World Examples
Car crashes and rocket launches rely on these principles to predict outcomes and ensure safety.
Key Formula
\[\vec{p} = m\vec{v}\]
Examples
Billiard balls colliding on a pool table demonstrate conservation of momentum.
A two-stage rocket uses momentum to separate and propel itself further.
In a Nutshell
Momentum and center of mass principles help us solve problems involving many interacting objects.