Lecture Notes by Walter Lewin

Introduction to Physics

• Lecturer: Walter Lewin
• Focus: Range of physical phenomena from subatomic to cosmic scales
• Measurement spans 45 orders of magnitude, from protons to the universe.

Fundamental Units

• Length: meter
• Time: second
• Mass: kilogram

Derived Units

• Commonly used derived units:
  • Centimeters, millimeters, kilometers
  • Inches, feet, miles
  • Astronomical units, light-years
  • Other time units: milliseconds, microseconds, days, weeks, months, years
  • Mass units: milligrams, pounds, metric tons

Units System Preferences

• Preference for decimal system over imperial (inches, feet) due to complexity

The Powers of Ten

• Introduction to a film called The Powers of Ten
• Explores the concept of scale – 40 orders of magnitude
• Concept originally conceived by Kees Boeke in the early 1950s

Fundamental Quantities in Physics

• Length: L
• Time: T
• Mass: M

Derived Quantities

• Speed: [L]/[T]
• Volume: [L³]
• Density: [M]/[L³]
• Acceleration: [L]/[T²] (e.g., m/s²)

Importance of Measurement Uncertainty

• Every measurement must include its uncertainty
• Uncertainty makes measurements meaningful
• Example experiment comparing lengths while standing vs. lying down
  • Measurements:
    • Standing: 183.2 cm ± 0.1 cm
    • Lying: 185.7 cm ± 0.1 cm
• Conclusion: Validates grandmother’s claim about height when lying down

Scaling Argument of Mammal Size

• Reasoning by Galileo Galilei on limits of mammal size based on bone strength
• Scaling of femur length and thickness in relation to mass
  • Length of femur (l) proportional to size (S)
  • Mass (M) proportional to size³
  • Pressure on the femur: P = M/A
  • Result: Femur thickness must increase more rapidly than length to support mass

Empirical Testing

• Tested the scaling argument with femur bones of various mammals from Harvard
• Expected vs. Actual results on d/l ratios
  • d/l for larger animals did not match predicted outcomes, leading to reevaluation of scaling laws.

Dimensional Analysis Example: Falling Apple

• Objective: Understand the fall time of an apple from different heights
• Time (t) to fall is proportional to height (h)
  • Proposed relation:
    • t ∝ h^α
    • Consider mass (m) and gravitational acceleration (g) also
• Results of dimensional analysis established that t is proportional to √h while m was not a factor

Experimental Verification

• Setup for dropping apples from various heights:
  • Height 1: 3 meters
  • Height 2: 1.5 meters
• Time measurements:
  • t1 = 781 ms ± 2 ms
  • t2 = 551 ms ± 2 ms
• Confirmed the theoretical prediction of t1/t2 ratio of √(h1/h2)

Key Insights and Closing Thoughts

• Measurements show that fall time is independent of mass
• The discussion illustrated the utility and limitations of dimensional analysis
• Understanding physics deeply involves recognizing its intricacies

Conclusion

• Reminder about the importance of measurement uncertainty and dimensional analysis in physics
• Encouragement to think critically about physical concepts and principles
• Next lecture: Friday

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• Key Takeaways:
  • Measurement uncertainty is fundamental.
  • Scaling laws provide insight into biological limitations.
  • Dimensional analysis can yield valuable insights but also has limitations.