Kinematics & Dynamics – Unit Systems, Relevance, and Foundations

Kinematics and Dynamics: Introductory Context

• Opening quotation highlights unity of sciences: “biology is chemistry, chemistry is physics, physics is life.”
  • Underscores how foundational physics principles pervade higher-level disciplines.
• MCAT students often perceive physics as abstract or “least medical,” largely because of calculus-heavy courses.
• Real-world clinical examples of physics in medicine:
  • Rehabilitation: analysis of motion, forces, bone strength (biomechanics).
  • Ophthalmology: ray-tracing diagrams for myopia & hyperopia.
  • Cell biology: mitochondria likened to “batteries” → literal connection to electrochemical potential & energy conversion.
• Chapter roadmap (what follows in the full text):
  • Review of three unit systems: MKS, CGS, SI.
  • Brief geometry & vector math refresher for problem-solving.
  • Transition into kinematics (equations of motion) and Newtonian dynamics (forces & their effects).

Why Units Matter

• Mathematics supplies numerical descriptions; units supply meaning.
• Without units, numbers are ambiguous—units act as the “vocabulary” of physics.
• Consistent unit usage prevents calculation errors and misinterpretation (crucial in clinical dosing, imaging calibrations, etc.).

Survey of Unit Systems Encountered on the MCAT

• Three headline metric frameworks:
  • MKS: meters–kilograms–seconds (macroscopic, common in mechanics & electromagnetism).
  • CGS: centimeters–grams–seconds (historically used in electromagnetism, occasionally appears in literature).
  • SI (International System of Units): incorporates MKS plus four additional base quantities.
• Non-metric system of note:
  • British/Imperial (FPS): feet–pounds–seconds; prevalent in U.S. daily life but virtually absent from MCAT passages.

British / Imperial (FPS) System

• Base quantities:
  • Length: foot $\text{ft}$
  • Weight (force): pound $\text{lb}$
  • Time: second $\text{s}$
• Because weight (a force) is fundamental, mass must be defined secondarily → slug or blob.
  • $1\,\text{slug}=1\,\text{lb}\,\text{s}^2\,\text{ft}^{-1}$
  • Alternate mass unit “blob” similarly defined but with inches.
• MCAT relevance: essentially none, but recognition prevents confusion if encountered.

Metric / SI Base Units (7 Total)

• Length: meter $\text{m}$
• Mass: kilogram $\text{kg}$ (note—mass, not weight)
• Time: second $\text{s}$
• Electric current: ampere $\text{A}=\text{C}\,\text{s}^{-1}$
• Amount of substance: mole $\text{mol}$
• Temperature: kelvin $\text{K}$ (absolute scale; no degree symbol)
• Luminous intensity: candela $\text{cd}$
• Significance: Any measurable physical quantity can be expressed as a product of these base units raised to powers.

Derived Units: Building Blocks from Bases

• Created by algebraic combinations of base units.
• Force (newton): $1\,\text{N}=1\,\text{kg}\,\text{m}\,\text{s}^{-2}$
• Work/Energy (joule): $1\,\text{J}=1\,\text{kg}\,\text{m}^2\,\text{s}^{-2}$
• Power (watt): $1\,\text{W}=1\,\text{kg}\,\text{m}^2\,\text{s}^{-3}=1\,\text{J}\,\text{s}^{-1}$
• CGS parallels:
  • Force → dyne $1\,\text{dyn}=1\,\text{g}\,\text{cm}\,\text{s}^{-2}$
  • Energy → erg $1\,\text{erg}=1\,\text{g}\,\text{cm}^2\,\text{s}^{-2}$
• FPS parallels:
  • Force still expressed directly in pounds; energy often foot-pounds.
  • Emphasizes why conversions can become cumbersome outside SI.

Table-Style Summary of Key Derived Units (verbal form for quick recall)

• Mass: slug (FPS) vs. gram (CGS) vs. kilogram (MKS/SI).
• Force: pound-force vs. dyne vs. newton.
• Work/Energy: foot-pound vs. erg vs. joule.
• Power: foot-pound per second vs. erg per second vs. watt.

Smaller-Scale (Atomic, Molecular, Sub-atomic) Units

• Length:
  • Angstrom $1\,\text{Å}=10^{-10}\,\text{m}$ (size of atoms, bond lengths).
  • Nanometer $1\,\text{nm}=10^{-9}\,\text{m}$ (protein dimensions, visible-light wavelength scale).
• Energy:
  • Electron-volt $1\,\text{eV}=1.6\times10^{-19}\,\text{J}$
  • Conceptual definition: energy gained by an electron accelerated through $1\,\text{V}$ of electric potential.
  • Common in particle, nuclear, and semiconductor physics; convenient order-of-magnitude in biophysics (ATP hydrolysis ~ $50\,\text{kJ mol}^{-1}\approx0.5\,\text{eV per molecule}$).

Vector Refresher (Preview)

• Although detailed mathematics appear in later sections, students are reminded that geometry—especially vector addition, components, and trigonometry—is foundational.
• Clinical analogies: calculating resultant muscle forces, determining net blood-flow vector in multi-vessel junctions, etc.

Ethical & Practical Implications

• Accurate unit usage safeguards patient safety (dosing, radiation exposure).
• Misinterpretation of unit conversions has historically led to catastrophic errors (e.g., Mars Climate Orbiter loss due to imperial–metric mismatch).
• Developing “unit literacy” is thus a professional responsibility for future clinicians and researchers.

Looking Ahead

• Mastery of units streamlines problem solving when tackling:
  • Kinematics equations (e.g.
    $v = v<em>0 + at$, $x = x</em>0 + v<em>0t + \tfrac12 at^2$, $v^2 = v</em>0^2 + 2a\Delta x$).
  • Newton’s laws in their quantitative form ($F = ma$).
• Subsequent chapters will delve into vectors, free-body diagrams, energy conservation, and rotational dynamics—all built on the unit framework established here.