Conservation laws are fundamental principles in physics that state certain quantities remain constant in isolated systems. An isolated system is one where no external forces act upon it, like objects inside a closed box. The three main conservation laws are energy conservation, momentum conservation, and angular momentum conservation. These laws help us understand and predict the behavior of physical systems, from simple pendulums to complex planetary motions.
Conservation of energy states that the total energy in an isolated system remains constant. Energy can transform between kinetic energy, which depends on motion, and potential energy, which depends on position. As shown in this bouncing ball example, when the ball is at maximum height, it has maximum potential energy and zero kinetic energy. As it falls, potential energy converts to kinetic energy. At the bottom, kinetic energy is maximum while potential energy is minimum. The total energy, shown by the red line, remains constant throughout the motion.
Conservation of momentum states that the total momentum of a system remains constant when no external forces act. Momentum is a vector quantity with both magnitude and direction, calculated as mass times velocity. In this collision example, car one with mass 1000 kilograms moves at 20 meters per second, giving momentum of 20000 kilogram meters per second. Car two with mass 800 kilograms moves in the opposite direction at 15 meters per second, giving momentum of negative 12000 kilogram meters per second. The total momentum before collision is 8000 kilogram meters per second, and this total momentum is conserved after the collision.
Angular momentum conservation states that when no external torques act on a system, the angular momentum remains constant. Angular momentum equals moment of inertia times angular velocity. When a figure skater pulls their arms inward, their moment of inertia decreases, so their angular velocity must increase to conserve angular momentum. This is why skaters spin faster when they pull their arms close to their body. Similarly, planets move faster when they are closer to the sun in their elliptical orbits, demonstrating conservation of angular momentum in celestial mechanics.
Conservation laws can be mathematically derived from fundamental physics principles. Momentum conservation follows from Newton's second law: when the net force equals zero, the rate of change of momentum is zero, therefore momentum remains constant. Energy conservation derives from the work-energy theorem and the concept of conservative forces. When forces are conservative, kinetic energy plus potential energy remains constant. These conservation laws are deeply connected to symmetries in nature through Noether's theorem, which states that every continuous symmetry corresponds to a conservation law. This profound connection shows that conservation laws are not just empirical observations, but fundamental consequences of the underlying symmetries of physical systems.