The Timpson Lyceum · University Physics II (2026) – Electricity & Magnetism

Newton's Laws, Atoms, and Charge – Lecture 1 (University Physics II)

Newton's Laws, Atoms, and Charge – Lecture 1

Overview

This lecture bridges the mathematical groundwork of physics with the first real ideas of electricity and magnetism. It reviews vectors, trigonometry, and units, then sets up Newtonian mechanics as a formal axiomatic system built on Newton's laws, before defining work and proving the work-energy theorem. It closes by introducing the microscopic picture of matter: atoms built from protons, neutrons, and electrons, the meaning of electric charge, and how charge behaves in conductors, insulators, and through induction. These last topics are the true starting point of the course — everything in electricity and magnetism rests on the properties of charge introduced here.

Key Concepts

Units. Numbers alone are meaningless in physics; a quantity needs a unit that ties it to something physical. The base units used in this course are the meter (length), second (time), and kilogram (mass), with the coulomb (charge) added once electricity begins. Most other quantities are combinations of these: velocity is $\text{m/s}$, acceleration is $\text{m/s}^2$.

Scalars vs. vectors. A scalar has only magnitude (mass, speed, distance). A vector has magnitude and direction (velocity, force). A vector is written $\vec{A}$; its components are $A_x$ and $A_y$, and its length (magnitude) is the unsubscripted $A$.

Vector decomposition. Given length $A$ and angle $\theta$, the components are recovered with trigonometry. Given components, the length comes from the Pythagorean theorem and the angle from the inverse tangent:

• $A_x = A\cos\theta$, $A_y = A\sin\theta$
• $A = \sqrt{A_x^2 + A_y^2}$, $\theta = \tan^{-1}\!\big(A_y / A_x\big)$

A vector has no fixed location in space — only a magnitude and direction — so it may be drawn wherever is convenient.

Newtonian mechanics as an axiomatic system. Space is modeled as $\mathbb{R}^3$, time as $\mathbb{R}$. The undefined primitives are position, time, mass, and force; a particle is an idealized point with a position $\vec{r}$ at a time $t$. Newton's laws are the axioms — empirically validated starting points, not things to be proved.

Newton's "zeroth" law (superposition). Forces are modeled as vectors and combine by vector addition. The net force is the vector sum of all individual forces.

Newton's first law. There exists a reference frame in which an object with zero net force keeps a constant velocity (zero acceleration). Such a frame is an inertial reference frame — intuitively, one that is not accelerating. A frame that accelerates is non-inertial: objects appear to move without any force acting on them. This law overturns Aristotle's idea that motion requires continuous pushing; with no net force, a moving object simply keeps moving.

Newton's second law. In an inertial frame, the net force equals mass times acceleration: $\sum \vec{F} = m\vec{a}$ It applies component by component: $\sum F_x = ma_x$, $\sum F_y = ma_y$, $\sum F_z = ma_z$.

Newton's third law. The force object A exerts on B equals the negative of the force B exerts on A: $\vec{F}_{A\to B} = -\vec{F}_{B\to A}$ — equal magnitude, opposite direction.

Force units. Since $F = ma$, force has units $\text{kg}\cdot\text{m/s}^2$, named the newton (N). One newton accelerates a 1 kg mass at $1\,\text{m/s}^2$.

Work. For a constant force, work is force times distance traveled, $W = Fs$ (distance along the path, not displacement — a round trip does positive work even though displacement is zero). For a varying force, work is the integral $W = \int \vec{F}\cdot d\vec{s}$, the area under a force-vs-distance curve. Work is measured in joules (J), where $1\,\text{J} = 1\,\text{N}\cdot\text{m}$.

Kinetic energy and the work-energy theorem. Kinetic energy is $K = \tfrac{1}{2}mv^2$. The net work done on an object equals its change in kinetic energy: $W = \Delta K = K_f - K_i$.

Scale of the universe. Physical sizes span enormous ranges, from the observable universe ($\sim 10^{27}\,\text{m}$) down to a proton ($\sim 10^{-15}\,\text{m}$) and beyond. A hydrogen atom is about $10^{-10}\,\text{m}$ across.

Atoms. All everyday matter is made of atoms — combinations of protons, neutrons, and electrons. The number of protons fixes the element (1 = hydrogen, 2 = helium, 6 = carbon, 8 = oxygen); this count is the atomic number. Protons and neutrons set the atomic mass. Masses: proton $\approx 1.67\times10^{-27}\,\text{kg}$, neutron almost identical, electron $\approx 9.11\times10^{-31}\,\text{kg}$ — under a thousandth of a proton, so electrons are treated as massless for an atom's mass. Same proton count with differing neutron counts gives isotopes. All protons are identical to one another, as are all neutrons and all electrons.

Charge. Charge is a primitive, defined only by its behavior. Protons carry positive charge, electrons an equal-magnitude negative charge, neutrons none. Like charges repel; opposite charges attract. The elementary charge magnitude is $e = 1.602\times10^{-19}\,\text{C}$ (coulombs), and all observable charge is an integer multiple of $e$. The positive/negative naming is Benjamin Franklin's convention — unluckily assigned, since the mobile carriers are actually the negative electrons.

Ions. A neutral atom has equal protons and electrons. Remove electrons and it becomes a positive ion; add electrons and it becomes a negative ion.

Conservation of charge. Charge is never created or destroyed, only moved. Charging an object means transferring electrons; a negative charge on one body implies an equal positive charge left elsewhere.

Conductors, insulators, semiconductors. Conductors (e.g. metal wire) hold their outer electrons loosely, letting charge spread almost instantly over the surface — not by one electron traveling far, but by a chain-reaction push from atom to atom. Insulators (e.g. rubber) grip their electrons tightly. Semiconductors fall between the two.

Induction. A charged object can attract a neutral one without contact. Bringing a negatively charged balloon near a wall pushes the wall's electrons slightly away, so each atom's near side turns slightly positive and is attracted to the balloon — which is why a rubbed balloon sticks to a wall. Polar molecules like water carry a permanent such separation (a dipole).

Worked Example

A box of mass $m = 40\,\text{kg}$ rests on a frictionless surface. Two people push it, each with a force of $100\,\text{N}$ directed at $45^\circ$ above and below the horizontal so the vertical components cancel and the box slides straight along $x$. Find the acceleration.

Each push contributes only its horizontal component, $F_x = F\cos\theta$. The net horizontal force drives the motion through Newton's second law, $\sum F_x = ma_x$, so $a_x = \big(\sum F_x\big)/m$.

The result is less than the $5\,\text{m/s}^2$ obtained when both push straight along $x$ with the full $100\,\text{N}$ — a sanity check, since pushing at an angle wastes part of each force.

Summary

• Quantities need units; the base units are the meter, second, kilogram, and (for this course) coulomb, with everything else built from them.
• Vectors carry magnitude and direction; decompose with $A_x = A\cos\theta$, $A_y = A\sin\theta$, recombine with $A = \sqrt{A_x^2 + A_y^2}$ and $\theta = \tan^{-1}(A_y/A_x)$.
• Newton's laws are the axioms of mechanics: forces add as vectors, $\sum\vec{F}=\vec{0}$ means constant velocity in an inertial frame, $\sum\vec{F}=m\vec{a}$, and forces come in equal-and-opposite pairs.
• Work is force times distance ($W=\int\vec{F}\cdot d\vec{s}$, in joules), and the net work on an object equals its change in kinetic energy, $W = \Delta\!\left(\tfrac{1}{2}mv^2\right)$.
• Atoms are protons, neutrons, and electrons; the proton count names the element, protons and neutrons carry the mass, and electrons are effectively massless.
• Charge is a conserved primitive in units of coulombs and integer multiples of $e = 1.602\times10^{-19}\,\text{C}$: like charges repel, opposites attract, and charge moves freely through conductors, barely through insulators, and can attract neutral matter by induction.