Conservation Laws in Physics to Know for AP Physics C: Mechanics (2025)

Conservation laws are key principles in physics that describe how certain quantities remain constant in closed systems. These laws—energy, momentum, angular momentum, mass, and electric charge—help us understand and solve problems in mechanics and various physical interactions.

1. Conservation of Energy

   • Energy cannot be created or destroyed; it can only be transformed from one form to another.
   • The total mechanical energy (kinetic + potential) in a closed system remains constant if only conservative forces are acting.
   • In inelastic collisions, kinetic energy is not conserved, but the total energy (including thermal energy) is conserved.
   • The work-energy theorem relates the work done on an object to its change in kinetic energy.
   • Understanding energy conservation is crucial for solving problems involving systems in motion and forces.

2. Conservation of Linear Momentum

   • The total linear momentum of a closed system remains constant if no external forces act on it.
   • Momentum is a vector quantity, defined as the product of an object's mass and its velocity (p = mv).
   • In collisions, the total momentum before the collision equals the total momentum after the collision, regardless of the type of collision (elastic or inelastic).
   • Impulse, the change in momentum, is equal to the force applied multiplied by the time duration of that force.
   • Conservation of momentum is essential for analyzing interactions in systems involving multiple objects.

3. Conservation of Angular Momentum

   • The total angular momentum of a closed system remains constant if no external torques act on it.
   • Angular momentum is defined as the product of an object's moment of inertia and its angular velocity (L = Iω).
   • In isolated systems, changes in the distribution of mass can lead to changes in rotational speed (e.g., a figure skater pulling in their arms).
   • Angular momentum conservation is crucial in analyzing rotational dynamics and systems involving circular motion.
   • Understanding angular momentum helps in solving problems related to rotating bodies and their interactions.

4. Conservation of Mass

   • Mass is conserved in a closed system; the total mass before a reaction or process equals the total mass after.
   • This principle is foundational in chemical reactions and physical processes, where mass is neither created nor destroyed.
   • In classical mechanics, mass conservation is often assumed, but in relativistic contexts, mass-energy equivalence (E=mc²) must be considered.
   • The conservation of mass is essential for balancing chemical equations and understanding stoichiometry.
   • Recognizing mass conservation aids in problem-solving across various physics applications.

5. Conservation of Electric Charge

   • Electric charge is conserved in isolated systems; the total charge before an interaction equals the total charge after.
   • Charge can be transferred between objects, but the net charge remains constant in a closed system.
   • The principle of charge conservation is fundamental in understanding electric circuits, electrostatics, and electromagnetic interactions.
   • In particle physics, charge conservation plays a critical role in determining the outcomes of particle interactions and decays.
   • Mastery of charge conservation is vital for analyzing electrical phenomena and solving related problems in physics.