Rucete ✏ AP Physics C In a Nutshell
5. Linear Momentum and Center of Mass
This chapter covers the principles of linear momentum, impulse, conservation of momentum, elastic and inelastic collisions, and the motion of the center of mass. It emphasizes problem-solving strategies involving collisions and center of mass movement.
Momentum and Impulse
• Linear momentum (p) = mv.
• Newton’s second law: Fnet = dp/dt.
• Impulse (J): the integral of force over time, equals change in momentum: J = Δp = FΔt (if F is constant).
• Units of momentum and impulse: kg·m/s = N·s.
Conservation of Momentum
• Total momentum is conserved if the net external force on the system is zero.
• Internal forces (like collision forces between objects) do not affect total system momentum.
• Conservation applies separately in each coordinate direction (x and y).
Types of Collisions
Elastic Collisions
• Momentum and kinetic energy are both conserved.
• Common in idealized systems like billiard balls or atomic collisions.
Inelastic Collisions
• Momentum is conserved, but kinetic energy is not.
• Some initial kinetic energy is transformed into internal energy (heat, deformation).
Perfectly Inelastic Collisions
• Colliding objects stick together after impact.
• Maximum possible loss of kinetic energy while conserving momentum.
Center of Mass (CM)
• The CM of a system moves as if all external forces act on a single point mass located at the CM.
• CM position (for discrete masses): xCM = (Σmₙxₙ)/(Σmₙ)
• If no external force acts, the CM moves with constant velocity.
• Internal forces (explosions, collisions) do not change CM motion.
Applications and Problem Solving with Center of Mass
• Analyze motion of entire systems by focusing on the center of mass rather than on individual particles.
• Explosion or separation problems: although internal forces act, momentum conservation applies to the whole system.
• In projectile motion, if a projectile breaks into pieces, the center of mass continues to follow the original parabolic trajectory.
Momentum in Multi-Particle Systems
• Total momentum of a system: ptotal = Σmₙvₙ
• Even when particles move internally, the vector sum of momenta remains constant if no net external force acts.
• Collisions can be solved by applying conservation of momentum separately in the x- and y-directions.
• For explosion problems, conservation of momentum helps determine velocities of fragments immediately after separation.
In a Nutshell
Momentum connects force and motion for systems and objects. Conservation of momentum is a powerful tool in collision and explosion problems, and understanding center of mass motion simplifies complex systems. Tracking energy transformations and vector components is essential for mastering momentum-based analysis in physics.