PHYS 017: College Physics Study Notes

PHYS 017: College Physics Study Notes

Week 2: Fundamental Concepts of Physics

WHAT IS PHYSICS?

  • Definition: Physics is the most fundamental of the sciences.

  • Goal: To learn how the Universe works at its most fundamental level and to discover the basic laws governing it.

  • Relation to Natural Science: Physics is a natural science focused on studying matter and its motion through space and time, along with related concepts such as energy and force.

As an Experimental Science

  • Nature of Physics: Physics is fundamentally experimental, relying on systematic observation, measurement, and controlled experiments to discover laws of nature.

  • Process: Transforms abstract theories into validated knowledge by testing hypotheses in laboratories to confirm, refine, or overturn existing models.

  • Empirical Foundation: Ensures physics is grounded in objective evidence.

Study of Laws and Theories

  • Laws: Describes generalized patterns in nature supported by scientific evidence and repeated experiments, often expressible in a concise mathematical equation (e.g., Newton's second law).

  • Theories: Provides explanations for patterns in nature, also supported by evidence and verified multiple times, sometimes with models (e.g., Newton's theory of gravity).

Study of Force, Matter, and Energy

  • Matter: Anything with mass and volume, ranging from subatomic particles to galaxies.

  • Energy: Capacity to perform work, involved in transferring or changing forms.

  • Force: Interactions that cause changes in the motion or deformation of matter.

WHY STUDY PHYSICS AS A PSYCHOLOGY MAJOR?

  • Studying physics can enhance skills and knowledge crucial for a psychology major, especially for fields such as research psychology, cognitive neuroscience, and experimental psychology.

Analytical and Quantitative Skills

  • Physics develops stronger analytical and quantitative skills:

    • Logical and systematic thinking

    • Comfortable use of equations and models

    • Data analysis and result interpretation

Understanding Neuroscience and Brain Imaging

  • Modern psychology's overlap with biology and physics:

    • Tools such as EEG, fMRI, MEG, rely on electromagnetic principles.

    • Understanding physics helps grasp the operational mechanisms of these brain imaging techniques.

Improved Statistical and Research Thinking

  • Physics teaches crucial research skills including:

    • Measurement precision

    • Error analysis

    • Complex system modeling

    • Hypothesis testing

Cognitive Science and Computational Psychology

  • Useful for interests in:

    • Artificial intelligence

    • Computational behavior modeling

    • Decision theory

    • Perception research

  • Physics-style mathematical modeling is key here.

Competitive Edge for Graduate Programs

  • Physics coursework can indicate strong analytical ability to admissions committees, suggesting competence in quantitive coursework.

Week 3: Laboratory, Measurement & Mathematics

Introduction to the Physics Laboratory

  • Importance of Laboratory Work: Reinforces understanding of fundamental concepts and principles while developing skills in scientific measurement.

  • Structure: Lecture followed by laboratory sessions.

General Laboratory Directions

  • Responsibility: Careful use of expensive equipment; checking equipment condition before experiments.

    • Report any missing or damaged equipment.

    • Set workstation in order post-experiment.

Preparation for the Laboratory

  • Prior reading of:

    • Experiment instructions

    • Relevant textbook sections

    • Questions at the end of the experiment for in-experiment reference.

Conducting Experiments

  • Laboratory experiments complement classroom theories, sometimes preceding them.

  • Treat experiments as discovery and confirmation of principles, not merely step-by-step procedures.

Observations and Data

  • Data collection must be headed with personal and experiment details.

    • Include all observations in suitable tabular format.

    • Real data readings from instruments define observations.

    • Use of instruments must reflect their precision limits.

Writing Reports

  • Components of a Lab Report:

    • Cover sheet with names and exercise title.

    • Purpose explanation.

    • Original data sheets, graphs as applicable.

    • All result calculations.

    • Discussion of results, uncertainties, comparisons with accepted values.

    • Answer all experimental questions.

Measurements

  • Definition: Measurements give quantitative information critical in chemistry and physics, comprising an amount, a unit, and an uncertainty.

  • Notation: Decimal or scientific. SI (International System) primarily employs base units such as meters, seconds, kilograms, and derived units like liters.

International System of Units (SI)


  • Base Units

    Base Quantity

    Unit Name

    Symbol


    Length

    Meter

    m


    Mass

    Kilogram

    kg


    Time

    Second

    s


    Electrical Current

    Ampere

    A


    Temperature

    Kelvin

    K


    Amount of Substance

    Mole

    mol


    Luminous Intensity

    Candela

    cd

    SI Prefixes


    • Common Prefixes:

      Prefix

      Symbol

      Meaning


      Tera-

      T

      $10^{12}$


      Giga-

      G

      $10^{9}$


      Mega-

      M

      $10^{6}$


      Kilo-

      k

      $10^{3}$


      Deci-

      d

      $10^{-1}$


      Centi-

      c

      $10^{-2}$


      Milli-

      m

      $10^{-3}$


      Micro-

      μ

      $10^{-6}$


      Nano-

      n

      $10^{-9}$


      Pico-

      p

      $10^{-12}$

      Scientific Notation

      • Explanation: Expresses numbers as a product of a coefficient (N) and $10$ raised to a power (n).

      • Format: Nimes10nN imes 10^n, where N is between 1 and 10, and n is a whole number.

      • Example: Distance from Earth to Sun is 1.5imes1011m1.5 imes 10^{11} m.

      Error and Uncertainty

      • Concept: No measurement is perfect; all have errors and uncertainties.

      • Implication: Conclusions depend on managing uncertainties. Uncertainties noted after the ± sign (e.g., 2.5ext±0.12.5 ext{ ± } 0.1).

      Types of Uncertainties

      • Sources: From measuring devices, measurement procedures, and the observed quantity.

      • Divisions:

        • Systematic Uncertainties: Consistently bias results one direction (e.g., equipment flaws).

        • Random Uncertainties: Result from measurement variations, are unbiased.

      Accuracy and Precision

      • Accuracy: How close a measurement is to the accepted value.

      • Precision: How close a series of measurements are to one another.

      Numerical Estimates of Uncertainties

      • Upper Bound Example: 46.5extcmext(uncertainty)±0.146.5 ext{ cm } ext{(uncertainty) } ± 0.1.

      • Digital Equipment: Inherent uncertainty tied to smallest digit measurement; e.g., for a scale showing two decimals, uncertainty is ext±0.01gext{ ± } 0.01 g.

      Propagation of Uncertainties

      • When adding/subtracting: Combined uncertainty is the sum of absolute uncertainties.

      • When multiplying/dividing: Combined relative uncertainty is the sum of relative uncertainties.

      Significant Figures (SF)

      • Definition: Consist of all certain digits plus one uncertain/estimated digit.

      Significant Figure Rules

      • General Rules:

        1. All nonzero digits are significant.

        2. Zeros between nonzero digits are significant.

        3. Left-end zeros are not significant.

        4. Right-end zeros without a decimal are not significant.

        5. Right-end zeros with a decimal are significant.

      Significant Figures in Addition and Subtraction

      • Result should be rounded to the least precise number's decimal place.

      Significant Figures in Multiplication and Division

      • Result should match the least number of significant figures in any measurement used.

      Rounding Rules

      • Round number by deciding on significant figures, applying common rounding rules:

        • If the next digit is less than 5, drop it.

        • If greater or equal to 5, increase the last significant figure by one.

      Mathematics: Metric System and Conversion


      • Metric System Units:

        Unit

        Equivalent


        1 cm

        10 mm


        1 dm

        10 cm

        Right Angle Trigonometry

        • Key Functions: Sine, Cosine, and Tangent based on Right-Angled Triangles.

          • Sine (sin): racextOppositeextHypotenuserac{ ext{Opposite}}{ ext{Hypotenuse}}

          • Cosine (cos): racextAdjacentextHypotenuserac{ ext{Adjacent}}{ ext{Hypotenuse}}

          • Tangent (tan): racextOppositeextAdjacentrac{ ext{Opposite}}{ ext{Adjacent}}

        Law of Sines

        • Description: Relates the lengths of sides of a triangle to the sines of its angles:

          • racaextsin(A)=racbextsin(B)=raccextsin(C)rac{a}{ ext{sin}(A)} = rac{b}{ ext{sin}(B)} = rac{c}{ ext{sin}(C)}

        • Use Cases: Finding angles or sides depending on known parameters.

        Law of Cosines

        • Description: Relates the lengths of sides of a triangle and the cosine of one of its angles:

          • Formula: a2=b2+c2−2bcextcos(A)a^2 = b^2 + c^2 - 2bc ext{cos}(A)

        • Use Cases: Determine angles or side lengths when two sides and the included angle are known.

        Vectors

        • Definition: Quantities that have both magnitude and direction (e.g., displacement, force, etc.).

        • Representation: Typically symbolized by an arrow above the variable (e.g., extbfdextbf{d} for displacement).

        • Example: Saying “displace 20 meters at 30 degrees to the west of north” fully describes the vector.

        Coordinate Systems and Vectors

        • Vectors on a Cartesian plane can be expressed in terms of their components along the x and y axes:

          • extbfA=Axextbfi+Ayextbfjextbf{A} = A_x extbf{i} + A_y extbf{j}

        Multiplication of Vectors

        • Types:

          • Dot Product (Scalar Product): Provides a scalar value.

          • Cross Product (Vector Product): Provides a vector perpendicular to the plane of the two vectors.

        Standard Model

        • Fermions (Matter Particles): Include quarks and leptons, basic building blocks of matter.

        • Bosons (Force-Carrying Particles): Include photons, gluons, and W/Z bosons.

        Quantum Mechanics

        • Focuses on behaviors of particles at atomic and subatomic levels:

          • Key ideas: Energy quantization, wave-particle duality, uncertainty principle.

        Conclusion

        • Physics is crucial across; it has real-world applications in various domains.

        • Its study enhances analytical skills, understanding of fundamental principles, and the ability to relate different concepts in the natural sciences.