The Timpson Lyceum · University Physics I (2025)

Introduction to University Physics I– Lecture 0 (University Physics I)

Overview

This opening lecture frames what physics is before any equations are introduced. It situates physics as the most foundational of the sciences, distinguishes the three modes of reasoning that scientists use, and then gives a precise definition of the scientific method in terms of those modes. It then grounds everything in measurement and units, since physics — unlike pure mathematics — must connect to the physical universe. The lecture closes by re-enacting Galileo's study of falling objects: starting from raw measurements, inductively building a model, and then using calculus to deduce velocity, acceleration, and the general equations of motion. The goal is to give a feel for how a model is built and tested, not to drill problems yet.

Key Concepts

Three types of reasoning

• Deductive reasoning: drawing conclusions that follow necessarily from premises — logical implications that are always true. Classic form: If all men are mortal, and Socrates is a man, then Socrates is mortal. The whole implication holds regardless of what the terms mean (if all A are B, and C is an A, then C is a B). Mathematics is built entirely on deduction.
• Inductive reasoning: observing many specific instances and generalizing to a rule. Release an unsupported object repeatedly, watch it fall each time, and conclude "unsupported objects fall." The generalization is never strictly proven, only supported by repeated observation.
• Abductive reasoning: the counterpart to induction — using known generalizations to infer the most likely explanation of a single observed instance (inferring a cause from an effect).

Where physics sits

• Logic underlies mathematics; mathematics and logic together underlie physics; and physics underlies every other science. Keep asking "how?" of any scientific claim (biology → chemistry → the movement of electrons) and you eventually arrive at physics.
• Nearly every everyday interaction reduces to gravity or electromagnetic forces (e.g., your hand doesn't pass through a table because electrons in each repel).
• In physics you are allowed to use both deductive and inductive reasoning — that is precisely what makes it a science rather than pure mathematics.

What science actually does (the method)

• Inductively reason from observable, quantifiable facts to a premise. Observable = more than one person can in principle observe it; quantifiable = it can be measured.
• Encode that premise in a mathematical model.
• Apply deduction (logic and math) to derive the model's consequences.
• Test those consequences against observation: agreement validates the model, disagreement invalidates it.

Measurement and units

• A number without units is meaningless in physics ("the shrimp is 19" says nothing). Every measured quantity carries units that tie it to the universe.
• The three base units used at the start of the course:
  • time — seconds (s)
  • length — meters (m)
  • mass — kilograms (kg)
• All other early quantities are combinations of these: velocity $\text{m/s}$, acceleration $\text{m/s}^2$, force $\text{kg}\cdot\text{m/s}^2$, energy $\text{kg}\cdot\text{m}^2/\text{s}^2$.
• Dimensionless units: a radian is an angle defined as arc length over radius, $\theta = d/r$ (meters/meters), so the units cancel — yet it is still built from base units. Degrees behave the same way.

Kinematic definitions (from calculus)

• Velocity is the time-derivative of position: $\displaystyle v = \frac{dx}{dt}$.
• Acceleration is the time-derivative of velocity: $\displaystyle a = \frac{dv}{dt}$.
• Reversing these, velocity is the integral of acceleration and position the integral of velocity, each picking up a constant of integration fixed by initial conditions.

Galileo's free-fall result

• For an object dropped from rest, measurements of distance fallen $y$ versus elapsed time $t$ reveal that $y/t^2$ is a constant.
• This yields the model $y = \tfrac{1}{2}g\,t^2$, from which $v = g\,t$ and $a = g$ — a constant acceleration, the acceleration due to gravity, $g \approx 9.8\ \text{m/s}^2$.

General equations of motion

• Starting only from "acceleration is the constant $g$," integration gives the general results (here for vertical motion, with $v_0$ and $y_0$ the initial velocity and position):

Galileo's drop-from-rest formula is just the special case $v_0 = 0,\ y_0 = 0$. A later consequence of this same framework: projectiles (with horizontal and vertical motion treated separately) trace a parabola.

Worked Example

Problem: An object is dropped from rest from a tall tower. How far has it fallen after $t = 2\ \text{s}$, and how fast is it moving at that instant? Use $g = 9.8\ \text{m/s}^2$.

Distance fallen from rest:

Speed at that instant (velocity from rest):

So after 2 seconds the object has fallen about $19.6\ \text{m}$ and is moving at about $19.6\ \text{m/s}$. (Using the lecture's rounded $g = 10$ for quick mental math gives $20\ \text{m}$ and $20\ \text{m/s}$, matching the pattern in the measured data.)

Summary

• Three reasoning modes — deductive (necessary implications), inductive (instances → generalization), and abductive (generalization → likely cause) — are the tools of science; physics uses both deduction and induction.
• Physics is foundational: every other science ultimately reduces to it, and most everyday phenomena come down to gravity or electromagnetic forces.
• The scientific method: inductively reason from observable, quantifiable facts to a premise, encode it as a mathematical model, deduce its consequences, and test them against observation to validate or invalidate the model.
• Everything is measured in units built from the three base units — seconds, meters, kilograms — and all early quantities (velocity, acceleration, force, energy) are combinations of these.
• Galileo's free-fall model: measurements show $y/t^2$ is constant, giving $y = \tfrac{1}{2}g\,t^2$, hence constant acceleration $g \approx 9.8\ \text{m/s}^2$.
• Using $v = dx/dt$ and $a = dv/dt$ (and integrating back), the special drop-from-rest case generalizes to $v = g\,t + v_0$ and $y = \tfrac{1}{2}g\,t^2 + v_0 t + y_0$.