10 Important Ideas in Physics
Physics is the scientific study of the basic rules that govern the universe. Because physicists like to be precise, they often express their ideas as mathematical equations. What follow are ten of the most important ideas in physics. These ideas have had a profound impact on how scientists view the universe and on the technologies people use every day.
Newton’s second law

What it says: Newton’s second law describes how forces affect motion. It states that acceleration of any object increases as the net force on that object increases, and acceleration decreases as the mass of the object increases. It’s commonly expressed as the equation F_{net} = ma.

Why it’s important: Newton’s second law is the cornerstone of classical mechanics. Ideas about momentum, work, and energy all come out of it. Scientists and engineers employ Newton’s second law when they consider the motions of objects ranging from molecules to cars to galaxies.
Newton’s universal law of gravitation

What it says: Newton’s universal law of gravitation states that the gravitational force between two objects increases with mass and decreases with distance. It’s more precisely expressed with the equation F_{g} = Gm_{1}m_{2}/r^{2}, where m_{1} and m_{2} are masses, r is the distance between them, and G is a fundamental gravitation constant.

Why it’s important: Newton’s universal law of gravitation showed that the same laws of physics that govern the fall of an apple also govern the motions of the moon and planets. It began the search for laws of nature that were precise, simple to express, and applied equally to all parts of the universe.
Conservation of momentum

What it says: The momentum of an object is that object’s mass multiplied by its velocity. The law of conservation of momentum states that the total momentum of all the objects in the universe never changes.

Why it’s important: The law of conservation of momentum helps you understand collisions between objects. The total momentum before a collision equals the total momentum after a collision. You can use this fact to understand how the velocities of objects before a collision relate to velocities after a collision. Conservation of momentum is important in billiards, car crashes, and collisions between subatomic particles.
Conservation of angular momentum

What it says: You can think of angular momentum as the total amount of spin that an object has. An object has more spin if it’s rotating faster or if it has more mass. Conservation of angular momentum states that the total spin of all the objects in the universe never changes. If one object reduces its spin, another object must increase its spin.

Why it’s important: The law of conservation of angular momentum helps describe the physics of rotating objects and objects moving in circles. It’s particularly important in astronomy. Moons, planets, stars, and galaxies are all rotating, and angular momentum helps you understand all this rotation.
Conservation of energy

What it says: You can think of energy as the ability to do physical work. The law of conservation of energy states that energy can never be created or destroyed; it can only be transferred and converted into different forms.

Why it’s important: The law of conservation of energy is important wherever energy is involved. At power plants, chemical and mechanical energy are transformed into electrical energy. Kitchen appliances transform electrical energy into thermal and mechanical energy. Automobile engines transform chemical energy into thermal and mechanical energy. In each of these cases, the law of conservation of energy governs the processes involved.
Maxwell’s equations

What they say: Maxwell’s equations describe the physics of electricity, magnetism, how electricity and magnetism relate to each other, and how electricity and magnetism relate to light and other forms of electromagnetic radiation (such as Xrays). Maxwell’s equations require some advanced mathematics: All four must be written with vector calculus notation.

Why they’re important: Maxwell’s equations provide the theoretical basis for all modern electric technology, including power plants, electric motors, microphones, speakers, and any kind of wireless transmitter or receiver (including cellphones, wifi, and GPS).
Einstein’s theory of relativity

What it says: Einstein showed that space, the passage of time, and mass are not absolute. Instead, all three vary depending on your speed. For example, time passes more slowly for you the faster you travel. Your mass also increases with speed. Because speeds are always measured relative to a frame of reference, Einstein’s theory is typically referred to as a theory of relativity.

Why it’s important: The most famous equation in physics, E = mc^{2}, comes from Einstein’s theory of relativity. This equation states that energy equals mass multiplied by the speed of light squared. This means that mass and energy are equivalent, although there’s a lot of energy in just 1 kilogram of mass; 1 kilogram of mass is equivalent to approximately 90 quadrillion joules of energy.
The quantum theory

What it says: It’s natural to think that quantities in physics can take on any value. For example, you expect that you could apply a force of 1 N, 2 N, or anything in between (such as 1.4235N) to an object. The quantum theory states that this is not true in all situations, however. For example, inside the atom, quantities such as energy and angular momentum are quantized, meaning those quantities can only take on certain discrete values.

Why it’s important: Quantum theory is an important part of the understanding of atomic structure today. Much of modern chemistry and subatomic physics is based on quantum theory, and it has had a profound impact on modern technology. For example, transistors, which are key components in modern computers, wouldn’t exist without scientists’ understanding of quantum theory.
The Schrodinger equation

What it says: Schrodinger’s equation states that the universe is ultimately based on probability. For example, you can’t know exactly when an unstable atomic nucleus will decay. You can only know the probability that the nucleus will decay in a certain amount of time. Like the quantum theory, Schrodinger’s equation is particularly important inside of atoms.

Why it’s important: Newton put forth an important idea when he developed his laws of motion: The fundamental laws of nature give absolute and exact predictions of observable reality. Schrodinger challenged this notion with his equation. Some scientists (including Schrodinger himself) have been fundamentally uncomfortable with this idea that the universe is based on probability, and there have been a number of (unsuccessful) attempts to develop newer theories in which the universe would be absolutely determined.
The standard model

What it says: The standard model describes and predicts all the fundamental (indivisible) particles that you can observe today, as well as all the fundamental forces except gravity. It’s a unified theory that includes electricity, magnetism, and nuclear physics. The standard model isn’t typically a part of introductory physics courses, but introductory physics students should at least be aware of its existence.

Why it’s important: The standard model represents the edge of scientists’ understanding of basic physics. Much of the research in basic physics over the last 50 years (including that done by the Large Hadron Collider) has been in testing the predictions of the standard model and in looking for ways to improve upon it.