[Sample Lesson] ▣ Chapter 1 - Introduction to Physics

1. Physics and the Laws of Nature

  • Physics: the study of the fundamental laws of nature
  • these laws can be expressed as mathematical equations
  • much complexity can arise from relatively simple laws

2. Units of Length, Mass, and Time

  • SI units of length (L), mass (M), time (T):
    • Length: the meter
      • Was: one ten-millionth of the distance from the North Pole to the equator
      • Now: the distance traveled by light in a vacuum in 1/299,792,458 of a second
    • Mass: the kilogram
      • One kilogram is the mass of a particular platinum-iridium cylinder kept at the International Bureau of Weights and Standards, Sèvres, France.
    • Time: the second
      • One second is the time for radiation from a cesium-133 atom to complete 9,192,631,770 oscillation cycles.

3. Dimensional Analysis

  • Any valid physical formula must be dimensionally consistent
  • Each term must have the same dimensions
    • Distance = velocity × time
    • Velocity = acceleration × time
    • Energy = mass × (velocity)²

4. Significant Figures

  • accuracy of measurements is limited
  • significant figures: the number of digits in a quantity that are known with certainty
  • number of significant figures after multiplication or division is the number of significant figures in the least-known quantity
  • Example:
    • A tortoise travels at 2.51 cm/s for 12.23 s. How far does the tortoise go?
    • Answer: 2.51 cm/s × 12.23 s = 30.7 cm (three significant figures)

 

❖ Scientific Notation

  • Leading or trailing zeroes can make it hard to determine number of significant figures: 2500, 0.000036
  • Each of these has two significant figures
  • Scientific notation writes these as a number from 1-10 multiplied by a power of 10, making the number of significant figures much clearer:
    • 2500 = 2.5 × 10³ If we write 2.50×10³, it has three significant figures 0.000036 = 3.6 x 10⁻⁵
  • Round-off error:
    • The last digit in a calculated number may vary depending on how it is calculated, due to rounding off of insignificant digits
    • Example:
      • $2.21 + 8% tax = $2.3868, rounds to $2.39
      • $1.35 + 8% tax = $1.458, rounds to $1.49
      • Sum:
        • $2.39 + $1.49 = $3.88
        • $2.21 + $1.35 = $3.56
        • $3.56 + 8% tax = $3.84

5. Converting Units

  • Converting feet to meters: 316ft = ? m
    • 1 m = 3.281 ft (this is a conversion factor)
    • Or: 1 = 1 m / 3.281 ft
    • 316 ft × (1 m / 3.281 ft) = 96.3 m
    • Note that the units cancel properly – this is the key to using the conversion factor correctly.

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