Foundations of Physics I: Units, Motion, and Measurement

Lecture 1: Introduction to Physics as a Scientific Discipline

What is Physics?

Physics is the scientific study of matter and energy, and how they interact. It seeks to understand the fundamental principles governing the natural world, often by making observations and conducting experiments.

• Physics I focuses on describing and predicting motion.

• Physicists break down complex phenomena into simple components and ignore minor effects to focus on core principles.

• Facts in physics can be classified as:

  • Type 1: Easily verifiable by simple observation.

  • Type 2: Established by experiments.

  • Type 3: Not all are simple assumptions; some require deeper analysis.

Describing and Predicting Motion

Physics I is primarily concerned with the description and prediction of motion, including:

• Motion of objects: Moving objects, moving fluids, moving energy (e.g., sound waves).

• Motion of fields: Electric and magnetic fields.

Units and Measurement in Physics

Importance of Units

Units are essential in science for quantifying observations and ensuring clarity in communication. Using correct units allows for accurate measurement and comparison of physical quantities.

• Basic (Simple) Units:

  • Length [L]: meter (m), centimeter (cm), kilometer (km), inch (in), foot (ft), mile (mi).

  • Time [T]: second (s), minute (min), hour (h), day, season.

  • Mass [M]: kilogram (kg), gram (g), milligram (mg), slug (imperial unit).

  • Angle: degree, radian, arcminute, arcsecond.

Compound Units

Compound units are constructed from basic units to express derived quantities.

• Examples:

  • Area: $[L]^2$ (e.g., m2, ft2)

  • Volume: $[L]^3$ (e.g., m3, cm3)

  • Density: $[M]/[L]^3$ (e.g., kg/m3)

  • Speed: $[L]/[T]$ (e.g., m/s, km/h)

• Compound units must make physical sense, not just mathematical sense.

Unit Conversion and Comparison

Unit conversion is a critical skill in physics, allowing comparison between different measurement systems.

• Example: Converting velocity from m/s to mi/hr.

• Conversion factor: $1~ ext{mi} = 1609~ ext{m}$

• Sample calculation:

$24~ ext{m/s} = 24~ ext{m/s} \times \frac{3600~ ext{s}}{1~ ext{hr}} \times \frac{1~ ext{mi}}{1609~ ext{m}} \approx 54~ ext{mi/hr}$

Describing Motion: Kinematics

Motion of a Point Particle

The simplest motion to analyze is that of a single point particle. To describe its motion, we need to specify its position at different times.

• Displacement: The change in position of a particle.

• Distance: The total length of the path traveled.

• Time Interval: $\Delta t = t_2 - t_1$

• Displacement: $\Delta x = x_2 - x_1$

Average Velocity

Average velocity is defined as the change in position divided by the change in time.

• Formula:

$V = \frac{\Delta x}{\Delta t}$

• Graphical interpretation: The slope of the line connecting two points on a position vs. time graph represents average velocity.

Instantaneous Velocity

Instantaneous velocity is the velocity of a particle at a specific moment in time, represented by the slope of the tangent to the position vs. time curve.

• On a graph, this is the slope at a single point.

Angular Motion and Angular Velocity

For rotational motion, we use angular displacement and angular velocity.

• Angular displacement: $\Delta \theta = \theta_2 - \theta_1$

• Average angular velocity: $\overline{\omega} = \frac{\Delta \theta}{\Delta t}$

Average Acceleration

Acceleration is the rate of change of velocity with respect to time.

• Formula:

$\overline{a} = \frac{\Delta v}{\Delta t}$

• In introductory physics, acceleration is often assumed to be constant.

Examples and Applications

Geometric Scaling Problem

Consider a cylindrical container "Y" and a second container "X" that is scaled up by a factor of 1.5 in all dimensions.

• Length: Scales by 1.5

• Circumference: Scales by 1.5

• Area: Scales by $1.5^2 = 2.25$

• Volume: Scales by $1.5^3 = 3.375$

• Example: If Y contains 250 L of H2O, X contains $250 \times 3.375 = 843.75$ L

Graphical Interpretation of Motion

Position vs. time and velocity vs. time graphs are essential tools for visualizing and interpreting motion.

• Linear graphs indicate constant velocity.

• Curved graphs indicate changing velocity (acceleration).

Summary Table: Basic and Compound Units

Quantity	Unit Symbol	SI Unit	Example
Length	[L]	meter (m)	1 m, 1 km, 1 ft
Time	[T]	second (s)	1 s, 1 min, 1 hr
Mass	[M]	kilogram (kg)	1 kg, 1 g
Area	[L]2	square meter (m2)	1 m2
Volume	[L]3	cubic meter (m3)	1 m3
Speed	[L]/[T]	meter per second (m/s)	10 m/s, 36 km/h
Density	[M]/[L]3	kg/m3	1000 kg/m3

Key Equations

• Displacement: $\Delta x = x_2 - x_1$

• Time Interval: $\Delta t = t_2 - t_1$

• Average Velocity: $V = \frac{\Delta x}{\Delta t}$

• Average Angular Velocity: $\overline{\omega} = \frac{\Delta \theta}{\Delta t}$

• Average Acceleration: $\overline{a} = \frac{\Delta v}{\Delta t}$

Additional info:

• Some context and terminology have been expanded for clarity and completeness.

• Examples and applications have been inferred and elaborated for academic depth.