Conserved Quantities: What Stays the Same in a Changing World
The Core Idea: Unchanging in the Midst of Change
Imagine you have a box of 10 building blocks. You can build a tall tower, a long wall, or a small house. No matter what you build, the number of blocks stays the same—10. You haven't created new blocks or destroyed any; you've just rearranged them. The quantity of blocks is conserved.
This simple idea is one of the most important in all of science. In nature, certain measurable properties are like the number of blocks in that box. Even when a system undergoes dramatic changes—like a car crash, a chemical explosion, or a star collapsing—these specific quantities remain unchanged. They are the universe's constants, the unwavering rules that every process must obey.
Fundamental Conserved Quantities in Physics
Scientists have identified several quantities that are universally conserved. Let's explore the most important ones.
1. Conservation of Energy
This is perhaps the most famous conservation law. Energy is the ability to do work or cause change. It can take many forms: kinetic (energy of motion), potential (stored energy), chemical, thermal (heat), and more. The law of conservation of energy states that energy cannot be created or destroyed; it can only be transformed from one form to another.
Example: A roller coaster at the top of a hill has a lot of potential energy. As it races down, that potential energy is transformed into kinetic energy, making the car go faster. At the bottom of the hill, the kinetic energy is at its maximum. Some energy is also transformed into heat and sound due to friction, but if you could add up all the energy—potential, kinetic, heat, and sound—the total would be the same as the potential energy the car had at the start.
2. Conservation of Momentum
Momentum is a measure of an object's motion and is calculated by multiplying its mass by its velocity ($p = m \times v$). The conservation of momentum is crucial for understanding collisions. In a closed system (with no external forces), the total momentum before a collision equals the total momentum after the collision.
Example: Imagine two ice skaters facing each other. If they push off each other, the skater with less mass will glide away faster than the skater with more mass. The product of mass and velocity (momentum) for the lighter skater increases in one direction, while for the heavier skater, it increases equally in the opposite direction. The total momentum remains zero, just as it was before they pushed off.
3. Conservation of Mass
In ordinary chemical reactions and physical processes, mass is conserved. This means the total mass of the substances involved in a reaction remains constant. The atoms are simply rearranged into new molecules.
Example: Burning a piece of wood seems to destroy it, leaving only ashes, which weigh much less. However, if you could trap all the gases (like carbon dioxide and water vapor) and smoke released during burning and add their mass to the mass of the ashes, the total would equal the original mass of the wood and the oxygen used from the air. This principle is the foundation for balancing chemical equations.
4. Conservation of Electric Charge
Electric charge, which can be positive or negative, is always conserved. This means that the net electric charge of an isolated system remains constant. Charge can be transferred (like when you get a shock from a doorknob), but it cannot be created or destroyed.
Example: When you rub a balloon on your hair, electrons (which carry negative charge) move from your hair to the balloon. The balloon becomes negatively charged, and your hair becomes positively charged. The net charge—the sum of the positive and negative charges—was zero before and remains zero after. Charge has been separated, not created.
| Conserved Quantity | What It Is | Simple Example |
|---|---|---|
| Energy | The capacity to do work. | A swinging pendulum: energy converts between kinetic and potential. |
| Momentum | Mass in motion ($p = m v$). | A rocket propelling forward as it expels exhaust backward. |
| Mass | The amount of matter in an object. | Mixing baking soda and vinegar: the total mass of ingredients is conserved. |
| Electric Charge | A fundamental property of matter. | Static electricity: charge is transferred, not created. |
Conservation in Action: From Playgrounds to Power Plants
Conservation laws are not just abstract ideas; they are at work all around us. Let's see how they apply in everyday life and technology.
Playing Pool: A game of pool is a perfect demonstration of momentum conservation. When the cue ball strikes another ball, it transfers some of its momentum. The paths and speeds of the balls after the collision can be predicted using conservation laws. The sound and heat generated from the impact account for the conservation of energy.
Generating Electricity: In a hydroelectric dam, the potential energy of water stored high up is converted into kinetic energy as it falls. This kinetic energy spins a turbine, which converts it into mechanical energy, and finally, a generator transforms it into electrical energy. Throughout this complex process, the total energy is conserved.
Cooking Food: When you light a gas stove, the chemical potential energy stored in the natural gas is released as heat and light through combustion (a chemical reaction). The mass of the gas and oxygen used equals the mass of the resulting carbon dioxide and water vapor, plus the soot if any. Mass and energy are both conserved in this everyday activity.
Common Mistakes and Important Questions
This is a common point of confusion. The law of conservation of energy says the total amount of energy in the universe is constant. Our "energy crisis" is not about energy disappearing. It's about the usability of energy. When we use energy, it often ends up as waste heat that is very difficult to capture and use again (this is related to a concept called entropy). So, we need to "save" high-quality, usable energy sources (like gasoline or electricity) because they are limited and valuable for doing specific tasks.
This is an excellent question that leads to a more advanced concept. In chemical reactions, mass is conserved to an extremely high degree of accuracy. However, in nuclear reactions (like those in the sun or a nuclear power plant), a tiny amount of mass is converted into a enormous amount of energy, as described by Einstein's famous equation, $E = mc^2$. In these extreme conditions, mass and energy together are conserved. We say that mass-energy is the truly conserved quantity. The separate conservation of mass is a very good approximation for most situations but not absolute.
Yes! This is a critical detail. Conservation laws typically apply to closed systems (or isolated systems). A closed system does not exchange the conserved quantity with its surroundings. For example, if you kick a soccer ball on Earth, its momentum is not conserved because your foot (an external force) is adding momentum to it. However, if you consider the system of "foot + ball" together, their total momentum during the brief moment of contact is conserved. So, defining the system correctly is essential for applying conservation laws.
Footnote
1 Entropy: A measure of the disorder or randomness in a system. In many natural processes, the total entropy increases, which explains why energy becomes less usable over time.
2 Closed System: A physical system that does not exchange any matter with its surroundings and may or may not exchange energy, depending on the definition. For strict conservation of a quantity like momentum, an isolated system (which exchanges nothing) is often required.
3 Net Charge: The sum of positive and negative charges within a system. For example, an object with 5 positive charges and 3 negative charges has a net charge of +2.