Conservation Laws

Conservation laws are fundamental principles in physics that state certain quantities remain constant over time within a closed system. These laws form the foundation of classical physics and remain valid even in modern physics.

Conservation of Energy

The total energy of an isolated system remains constant. Energy can be transformed from one form to another but cannot be created or destroyed.

Etotal=Ekinetic+Epotential=constantE_{total} = E_{kinetic} + E_{potential} = constant
12mv2+mgh=constant\frac{1}{2}mv^2 + mgh = constant

Conservation of Linear Momentum

In the absence of external forces, the total linear momentum of a system remains constant.

p⃗total=∑miv⃗i=constant\vec{p}_{total} = \sum m_i\vec{v}_i = constant
m1v⃗1+m2v⃗2=m1v⃗1′+m2v⃗2′m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{v}'_1 + m_2\vec{v}'_2

Conservation of Angular Momentum

In the absence of external torques, the total angular momentum of a system remains constant.

L⃗=r⃗×p⃗=constant\vec{L} = \vec{r} \times \vec{p} = constant
Iω=constantI\omega = constant

Conservation of Mass-Energy

While mass and energy are separately conserved in classical physics, Einstein's special relativity showed they are actually different forms of the same quantity.

E=mc2E = mc^2

Applications

  • Collision analysis
  • Orbital mechanics
  • Fluid dynamics
  • Thermodynamic processes
  • Mechanical systems