Physics Lecture by Walter Lewin

Introduction

• Instructor: Walter Lewin
• Focus: From the very small (fraction of a proton) to the very large (the universe).
• Span of Magnitude: 45 orders of magnitude.

Introduction to Units

• Fundamental Units: Length (meter), Time (second), Mass (kilogram)
• Derived Units:
  • Length: centimeters, millimeters, kilometers, inches, feet, miles, astronomical unit, light-years
  • Time: milliseconds, microseconds, days, weeks, hours, centuries, months
  • Mass: milligrams, pounds, metric tons

Fundamental Quantities in Physics

• Symbols:
  • Length: L
  • Time: T
  • Mass: M
• Derived Quantities:
  • Speed: [L]/[T] (dimension of length per time)
  • Volume: [L]^3
  • Density: [M]/[L]^3
  • Acceleration: [L]/[T]^2
  • Units: meters/second^2

Importance of Measurement Uncertainty

• Key Principle: Any measurement without knowledge of its uncertainty is meaningless.

Demonstration of Measurement Uncertainty

• Experiment: Measuring the length of an object standing up vs lying down
  • Tool: Aluminum bar for calibration
  • Measurements: 149.9 cm vertically (±1 mm), 150.0 cm horizontally (±1 mm)
  • Conclusion: Standing and lying lengths are nearly the same.

Practical Measurement: Volunteering Student

• Example: Measuring a student standing vs lying down
  • Name: Zach
  • Standing Measurement: 183.2 cm (±0.1 cm)
  • Lying Down Measurement: 185.7 cm (±0.1 cm)
  • Conclusion: About 2.5 cm taller lying down.

Galileo Galilei's Scaling Argument

• Question: Why mammals are not much larger?
  • Reasoning: Too massive mammals would break their bones.

Scaling in Mammals

• Variables:
  • Size: S
  • Mass: M
  • Femur Length: l
  • Femur Thickness: d
• Scaling Argument:
  • Length of femur proportional to size
  • Mass proportional to volume (size^3)
  • Pressure on femur = Weight / Cross-section area
  • Mass proportional to d^2 (where d is thickness)

Scaling Result

• Derived Conclusion: Thickness of femur ∝ l^(3/2)
  • Scenario: Elephant vs Mouse

Experimental Verification

• Femurs of Various Animals: Measured femurs from raccoon to elephant.
  • Conclusion: No significant difference in d/l ratios between small and large mammals.

Dimensional Analysis

• Example: Dropping an apple from different heights
  • Variables:
    • Height: h (∝ h^α)
    • Mass: m (∝ m^β)
    • Gravity: g (∝ g^γ)
  • Dimensional Equation: T ∝ √(h/g) where α = 1/2, β = 0, γ = -1/2.
• Experiment Confirmation
  • Setup: Dropping apples from 3m and 1.5m heights
  • Results: Times measured accurately reflected predicted times.

Comparative Dimensional Analysis

• Alternate Analysis: Introducing mass of the Earth
  • Analysis fails indicating our initial approach was better.

Conclusion

• Importance of Dimensional Analysis: Shows application and limitations.
• Encouragement: Reflect on the differences in approaches.
• Lecture End: See you Friday!