College Physics Chapter 1: Models, Measurements, and Vectors Notes

• Standards and Units: Learn to understand basic units and how to change one unit to another accurately.

• Significant Figures: Know how to show measurements and calculations with the right amount of detail to show accuracy.

• Vector Operations: - Learn to add and subtract arrows (vectors) both on paper and through calculations.

  • Break down arrows into their horizontal (x) and vertical (y) parts.

The Nature of Physics and Measurement

• Experimental Science: Physics is about doing experiments and watching how things happen in the real world.

• Process of Science: - Watch what occurs in nature.

  • Make guesses based on what you see.

  • Scientific Frameworks: Organize information into Models, Hypotheses, Theories, and Laws.

Cultural and International Standards of Measurement

• Cultural Units: Units were often based on cultural standards like the "foot" or "mile," which could change based on where you were and when it was.

• The Système International (SI): - Started in 1889 to make measuring standards the same around the world.

• Three Fundamental S.I. Units: - Time: Second ($s$).

  • Length: Meter ($m$).

  • Mass: Kilogram ($kg$).

Definition and Evolution of Base Units

• The Second ($s$): - Initially defined as related to a day.

  • Now defined very precisely using atomic clocks with cesium atoms.

• The Meter ($m$): - Originally one ten-millionth of the distance from the North Pole to the Equator.

  • Now linked to how fast light travels.

• The Kilogram ($kg$): - Currently based on a physical object in France, but scientists want to replace this with a more modern atomic standard.

Unit Adjustments and Powers of Ten

• Scaling Units: Units can change to deal with really big or small numbers.

  • Example: Instead of saying how many meters it is from San Francisco to Charlotte, we say it's about 4,621 kilometers ($km$).

• Prefixes for Powers of 10: - Here are some prefixes you might see:

  • $10^{-3}$: milli- (m)

  • $10^{3}$: kilo- (k)

  • $10^{6}$: mega- (M)

Conversion Strategies and Derived Units

• Consistency in Calculation: You might find different measurement styles, but you need to convert everything back to meters, kilograms, and seconds for it to work together.

• Derived Units: - Units made from the base units.

  • Example: The energy unit is the Joule ($J$). If you use grams or centimeters instead of standard units, your answer will be wrong.

Calculation Example: Alpha Centauri

• Scenario: Alpha Centauri is $4.3$ light-years away, and we want to find out how far that is in kilometers.

• Concepts Required: - Light-years tell you the distance light travels in a year.

  • Use the formula: $\text{Distance} = \text{Time} \times \text{Speed}$, using the speed of light.

Precision and Significant Figures

• Limitations of Tools: All measuring tools can be inaccurate. Make sure your results match the detail your tools can give.

• Significant Figure (SF) Integrity: - Reporting every little digit from a calculator can create confusion.

  • Example: Dividing 10 (one detailed figure) by 3 (one detailed figure) gives 3.3333 on a calculator.

  • Reporting all those digits makes it seem way more precise than it really is.

Vector Addition and Components

• Vector Principles: When adding arrows, you can’t just add the lengths because direction matters too.

• Vector Deconstruction: - Long arrow ($\text{A}$) can be separated into horizontal ($A_x$) and vertical ($A_y$) parts.

  • Calculation for horizontal is $A_x = A \times \text{cos}(\theta)$ and for vertical is $A_y = A \times \text{sin}(\theta)$.

  • To find total length: $A = \text{sqrt}(A_x^2 + A_y^2)$.

• Example 1.7 Vector Addition Analysis: - Vector A: Length of $50$cm, angle of $30^{\text{°}}$.

  • Vector B: Length of $35$cm, angle of $110^{\text{°}}$.