Physics Essentials

The cards are designed for anyone taking their first steps in physics, whether you're a high school student working through an introductory course, a college beginner revisiting the basics, or simply someone curious about how the physical world is described. Even if you've encountered these ideas before, the deck serves as a quick refresher to make sure the key definitions and principles are firmly in place before you move on to more advanced material.

Because these concepts build on one another, it helps to work through the cards in order the first time, so that ideas like velocity and acceleration are familiar before you meet Newton's laws. After that, regular short review sessions are far more effective than occasional long cramming — physics vocabulary sticks best when you revisit it little and often. Try relating each term to something you see in everyday life, like feeling friction when you push a book across a table, and the definitions will feel much more natural than something simply to memorize.

Physics is the fundamental natural science concerned with matter, its motion and behavior through space and time, and the related concepts of energy and force. To describe these phenomena quantitatively, physicists rely on a shared system of measurement: the Système International d'Unités, or SI. The seven base SI units cover the fundamental dimensions needed in physics. Length is measured in metres, mass in kilograms, and time in seconds. Electric current is measured in amperes, thermodynamic temperature in kelvins, amount of substance in moles, and luminous intensity in candelas. All other physical quantities can be expressed as combinations of these base units.

A central distinction in physics is between scalar and vector quantities. Scalars have only magnitude, such as mass or temperature, while vectors have both magnitude and direction, such as velocity or force. Vectors are often represented by arrows whose length indicates magnitude and whose orientation indicates direction. Closely related to this is the difference between distance and displacement. Distance is a scalar representing the total length of the path traveled, while displacement is a vector pointing straight from the initial position to the final position. Because displacement depends only on the endpoints, it can be zero even when the distance traveled is significant, as in any journey that ends where it began.

The description of motion, or kinematics, is built on the concepts of speed, velocity, and acceleration. Speed is the scalar rate at which distance is covered, while velocity is the vector rate of change of displacement. Average speed equals total distance divided by elapsed time, whereas average velocity equals displacement divided by time. Acceleration is the rate of change of velocity with time, and because velocity is a vector, acceleration can arise from changes in magnitude, in direction, or in both. When acceleration is constant in magnitude and direction, three equations of motion apply. In these equations, \(u\) is the initial velocity, \(v\) is the final velocity, \(a\) is the acceleration, \(s\) is the displacement, and \(t\) is the time, so that \[v = u + at,\] \[s = ut + \tfrac{1}{2}at^2,\] and \[v^2 = u^2 + 2as.\]

The behavior of objects under the influence of forces is described by Newton's three laws of motion. The first law, sometimes called the law of inertia, states that an object at rest remains at rest, and an object in motion continues with constant velocity, unless acted upon by a net external force. This property of resisting changes in motion is what we call inertia. Newton's second law quantifies the effect of a net force: the net force on an object equals its mass multiplied by its acceleration, written as \(F_{\text{net}} = ma\). Acceleration is directly proportional to the applied force and inversely proportional to the mass of the object. Newton's third law completes the picture by noting that forces always come in pairs: for every action, there is an equal and opposite reaction, with the two forces acting on different objects.

It is important to distinguish between mass and weight. Mass is the amount of matter in an object, measured in kilograms, and is invariant regardless of location. Weight, in contrast, is the gravitational force acting on that mass, given by \(W = mg\), where \(g\) is the local gravitational field strength. Because \(g\) varies from place to place, an object's weight can differ while its mass remains the same. Among the contact forces encountered in everyday life, friction plays a major role. Friction is the force that opposes relative motion between two surfaces in contact. Static friction prevents motion from beginning, while kinetic friction acts once surfaces are sliding, and both are typically proportional to the normal force pressing the surfaces together.

On a universal scale, gravity is described by Newton's law of universal gravitation, which states that every particle in the universe attracts every other particle with a force given by \(F = G m_1 m_2 / r^2\), where \(G\) is the gravitational constant and \(r\) is the distance between the centers of the two masses. The force acts along the line joining the two particles. This single law, together with Newton's laws of motion, explains everything from the falling of an apple to the motion of planets around the Sun.

When a force acts on an object that moves, it does work. The work done by a constant force is defined as the product of the magnitude of the force, the magnitude of the displacement, and the cosine of the angle between them, so that \(W = Fd\cos\theta\). Work is a scalar quantity measured in joules, where one joule equals one newton-meter. When the force is parallel to the displacement, \(\cos\theta = 1\) and the work is maximum, while when the force is perpendicular to the motion, no work is done at all. Power measures how quickly work is done or how rapidly energy is transferred.

Average power is the work done divided by the time taken, \(P = W/t\), and for a constant force applied to a moving object, it can equally be written as \(P = Fv\). The SI unit of power is the watt, with one watt equal to one joule per second. A higher power rating means the same amount of work is accomplished in less time, which is why a powerful engine can accelerate a car faster than a weak one.

The concept of energy is closely tied to work. An object in motion possesses kinetic energy, given by \(KE = \tfrac{1}{2}mv^2\), which depends on the square of the speed and is the same whether the motion is to the left or to the right. An object raised to a height in a gravitational field has gravitational potential energy, \(PE = mgh\), where \(h\) is the height above a chosen reference level. In the absence of non-conservative forces such as friction or air resistance, the total mechanical energy, the sum of kinetic and potential energy, remains constant: this is the principle of conservation of mechanical energy. Energy can change form between kinetic and potential, but the total stays the same.

Linear momentum is the product of an object's mass and its velocity, written as \(\vec{p} = m\vec{v}\), and is a vector quantity whose direction matches the direction of motion. When a net force acts on an object, the change in momentum over a time interval equals the impulse delivered. In any closed system where no external forces act, the total linear momentum is conserved. This principle is invaluable for analyzing collisions, where the combined momentum of the colliding objects before the event equals the combined momentum after.

When an object moves in a circle at constant speed, the motion is called uniform circular motion. Even though the speed is constant, the direction of the velocity changes continuously, so the object is accelerating. This centripetal acceleration is directed toward the center of the circle and has magnitude \(a_c = v^2/r\). The force responsible for this acceleration, the centripetal force, is also directed toward the center and is provided by some real physical interaction such as tension, gravity, or friction.

Rotational motion has its own set of quantities analogous to those in linear motion. Torque is the rotational equivalent of force, given by \(\tau = rF\sin\theta\), and is the cause of angular acceleration. The moment of inertia \(I\) plays the role of mass for rotation, defined for a collection of point masses as \(I = \sum m r^2\), where each \(r\) is the perpendicular distance from the axis of rotation. Angular momentum, \(L = I\omega\) for a rigid body or \(L = r \times p\) more generally, is conserved whenever no external torque acts on a system. Pressure in fluids is defined as force per unit area, \(P = F/A\), and acts equally in all directions at a point in the fluid. Archimedes' principle states that the buoyant force on a submerged or floating object equals the weight of the fluid displaced; an object floats when the buoyant force is at least equal to its weight.

Temperature describes the state of thermal equilibrium between systems. Two common scales are used in physics. The Celsius scale fixes the freezing point of water at 0 °C and the boiling point at 100 °C, while the Kelvin scale is the absolute thermodynamic scale with its zero at absolute zero, the lowest possible temperature. Conversion between the two is straightforward, with \(T(\text{K}) = T(°\text{C}) + 273.15\). Heat is the energy transferred between objects at different temperatures, and the amount of heat required to change the temperature of a substance is given by \(Q = mc\Delta T\), where \(c\) is the specific heat capacity, a property that varies from material to material.

The laws of thermodynamics formalize the behavior of energy and heat. The zeroth law establishes the concept of temperature itself: if two systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other. This seemingly obvious statement allows temperature to be used as a consistent, comparable quantity. The first law is a statement of energy conservation applied to thermodynamic systems: the change in internal energy \(\Delta U\) of a system equals the heat \(Q\) added to the system minus the work \(W\) done by the system, written \(\Delta U = Q - W\). The second law introduces the concept of entropy, a measure of disorder or of energy that is no longer available to do useful work. In any spontaneous process, the total entropy of the universe either increases or stays the same, with \(\Delta S_{\text{universe}} \geq 0\).

For a gas that is dilute and at moderate temperature and pressure, the ideal gas law gives a simple relationship among pressure, volume, temperature, and amount of substance, expressed as \(PV = nRT\), where \(R\) is the universal gas constant. This law is a good approximation for many real gases and is a powerful tool for analyzing thermodynamic processes.

A wave is a disturbance that propagates through space and time, transferring energy from one place to another without any net transport of matter. Waves are characterized by their wavelength, frequency, and speed. Two main types of waves are distinguished by the direction in which the medium's disturbance occurs relative to the direction of propagation. In transverse waves, the oscillations are perpendicular to the direction of wave travel, as in light or waves on a string. In longitudinal waves, the oscillations are parallel to the direction of travel, as in sound. For all waves, the speed equals the product of frequency and wavelength, with \(v = f\lambda\).

Sound travels through gases, liquids, and solids as a longitudinal wave. In an ideal gas, its speed is given by \(v = \sqrt{\gamma P/\rho}\) or, equivalently, \(v = \sqrt{\gamma RT/M}\), where \(\gamma\) is the ratio of specific heats, \(P\) is pressure, \(\rho\) is density, \(T\) is absolute temperature, and \(M\) is the molar mass. In air at 20 °C, the speed of sound is approximately 343 m/s. When a source of sound and an observer move relative to each other, the observed frequency shifts. This is the Doppler effect, described by \(f' = f(v \pm v_o)/(v \pm v_s)\), where the signs depend on whether the observer or source is moving toward or away from the other. The familiar change in pitch of a passing siren is a common example.

Oscillatory motion of a particular kind is called simple harmonic motion, or SHM. In SHM, the restoring force on an object is directly proportional to the displacement from equilibrium and points back toward it, giving \(F = -kx\). The corresponding acceleration is \(a = -\omega^2 x\), where \(\omega\) is the angular frequency. A simple pendulum, when its amplitude is small, is an excellent approximation to SHM, and its period depends only on its length and the local gravitational acceleration, with \(T = 2\pi\sqrt{L/g}\). Notably, the period of a simple pendulum is independent of the mass of the bob and, for small oscillations, of the amplitude.

Light is an electromagnetic wave, and its interaction with matter is described by a small number of rules. When light strikes a smooth surface such as a mirror, it reflects such that the angle of incidence equals the angle of reflection. When light passes from one medium into another, it changes speed, and this speed change causes the light to bend at the interface. This bending is called refraction, and it is described by Snell's law, \(n_1\sin\theta_1 = n_2\sin\theta_2\), where the indices \(n\) are the refractive indices of the two media. The photoelectric effect, in which light shining on a metal ejects electrons, provided crucial evidence that light can behave as discrete packets of energy called photons, with each photon's energy given by \(E = hf\), where \(h\) is Planck's constant and \(f\) is the frequency.

Electricity describes the behavior of electric charges, which come in two types, positive and negative, and are conserved in all interactions. The fundamental force between two point charges is given by Coulomb's law, \(F = kq_1q_2/r^2\), with \(k = 9 \times 10^9 \text{ N·m}^2/\text{C}^2\); the force is repulsive for like charges and attractive for unlike ones. An electric field \(\vec{E}\) at a point in space is defined as the force per unit positive test charge at that point, and for a single point charge it is \(\vec{E} = kq/r^2\) in the radial direction. The electric potential \(V\) at a point is the work per unit charge required to bring a test charge from infinity to that point, and the potential energy of a charge \(q\) at a point is \(U = qV\).

Electric current is the rate of flow of charge, \(I = \Delta Q/\Delta t\), measured in amperes, and conventional current is taken to flow from positive to negative potential. Ohm's law relates the voltage across a resistor to the current through it as \(V = IR\), where \(R\) is the resistance in ohms. In a series circuit, the same current flows through every component and the voltages across components add, while in a parallel circuit, the same voltage appears across each branch and the currents add. A magnetic field \(\vec{B}\) exerts forces on moving charges and on current-carrying wires, with directions given by the right-hand rule and measured in teslas. Faraday's law of induction states that a changing magnetic flux through a loop induces an electromotive force, \(\mathcal{E} = -d\Phi_B/dt\), the operating principle behind electric generators. Modern physics extends classical understanding in two major ways. Special relativity rests on two postulates: the laws of physics are the same in all inertial reference frames, and the speed of light in vacuum, \(c\), is the same for all observers regardless of the motion of the source. From these postulates follow remarkable effects such as time dilation, in which a moving clock runs slow by a factor of \(1/\sqrt{1 - v^2/c^2}\), so that \(\Delta t = \Delta t_0/\sqrt{1 - v^2/c^2}\), where \(\Delta t_0\) is the proper time measured in the clock's own rest frame.