Physics Ch1

Key Ideas:
- Units
- Base Units
- System of Units
- Dimensional Analysis
- Conversion of Units
- Order of Magnitude Estimates
- Significant Figures

Definition: The study of the natural world.
Objectives:
- Develop models that represent idealized conceptions of the universe.
- Examples of models include:
- Big Bang Model
- Newtonian Mechanics
- Testing Models:
- Involves making measurements to verify the predictions made by these models.
Importance of Measurements:
- Measurements are critical for testing physical models.

A measurement consists of:
- A Number: Represents the magnitude of the quantity being measured.
- A Unit: A standard quantity used in measurement.
Dimensions:
- If the measurement number depends on the unit, it is said to have dimensions.
Examples of Units:
- Inches (in)
- Centimeters (cm)
- Furlongs
Agreement on Units:
- For a measurement to be meaningful, there must be consensus on the units used.
Base Units:
- A unit that is broadly accepted and agreed upon.
- Example of equivalences: 12" = 30.5 cm = 1.52 x $10^{-3}$ furlongs.

Definition:
- Any measurement will consist of one or a combination of seven base units.
The Seven Base Units include:
1. Length: Meter (m)
2. Time: Second (s)
3. Mass: Kilogram (kg)
4. Electric Current: Ampere (A)
5. Temperature: Kelvin (K)
6. Amount of Substance: Mole (mol)
7. Luminous Intensity: Candela (cd)
System Internationale (SI):
- The primary system of units used in PHYS 110 is the SI system.

Definition of Base Units:
- Base units are agreed-upon units of measure.
Examples of Definitions:
- Mass: The kilogram is defined by the weight of a platinum-iridium cylinder at the International Bureau of Weights and Measures.
- Time: Measured in seconds (s), defined as 1 second equaling 9,192,631,770 periods of microwave radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.
Dimensional Analysis:
- How to convert from one system of units to another.

Definition:
- A technique used to check, develop, or derive equations by treating dimensions as algebraic quantities.
Examples for Practice:
- Example 1.1: Check kinematics equation using dimensional analysis.
- Example 1.2: Derive kinematics equation using dimensional analysis.
Limitations:
- Dimensional analysis can establish the proper dependence on algebraic quantities but cannot derive constants of proportionality.

Unit Conversions:
- Can be effectively executed using dimensional analysis.
- Concept: Anything can be multiplied by the dimensionless number 1.
- Process:
- Express the number 1 as a ratio that maintains the desired dimensions.
- Perform one conversion at a time until all desired units are achieved.
Example 1.3:
- Convert the speed of a horse and buggy traveling 1200 furlongs per fortnight into SI units.
- Importance: Mastery of this skill is expected throughout the course.

Contextual Example:
- Compares gas company pricing corrections by volume at 15°C (as indicated on gas pumps).
Purpose:
- Often, approximate results are more useful than exact answers.
- Uses include:
- Quick calculations to verify more complex results.
- Engaging discussions with peers.

Definition:
- Expressed in scientific notation; assesses how large a number is compared to powers of 10.
Rules for Approximation:
- If the multiplier is less than $ ext{√10}$, the order of magnitude is that power of 10.
- If the multiplier is greater than $ ext{√10}$, the order of magnitude is one larger than the power of 10.
Symbol:
- Tilde (~) is used to represent the order of magnitude.

Example 1.4:
- Estimation of aluminum waste from beer cans produced in Dr. Reid's lifetime.
Aspect of Consideration:
- Factors include the thermal expansion of gas and the annual average temperature affecting gas sales in Canada.

Importance:
- Measurements help validate physical models in physics, and instruments introduce inherent measurement errors.
Significant Figures:
- Reported to indicate the precision and reliability of measurements.
- Example Measurements:
- L = 11 mm
- L = 11.3 mm
- L = 11.32 mm
- L = 11.325 mm
Error Tracking:
- Significant figures enable tracking of errors in measurements.

Principle: Knowing measurement error is crucial for drawing accurate conclusions from experimental data.
Example Process:
- Measure the circumference of a circle using the radius.
##### Measurement Example:
- Radius (R) = 10.1 cm (3 significant figures).
- Circumference (C) Calculation: C = 2R = 2 (10.1 cm) = 63.4601716…. cm.
Reporting Figures:
- Considering significant figures, C is reported as 63.5 cm to reflect that the radius measurement (R) has 3 significant figures, indicating confidence in the third digit.

Multiplication/Division: Report answer to the same number of significant figures as the number with the least significant figures in the product or quotient.
Addition/Subtraction: The answer should be reported to the number of decimal places in the sum that is smallest.
Function of Measurement: Report to the same significant figures as the argument in a function.
- Example: $ an(55.0) = 1.43$.
Dealing with Ambiguity in Values:
- In decimal representation, the number of significant figures can be indicated as follows:
- 12100 has 3 significant figures.
1. has 5 significant figures.
- 12100.00 has 7 significant figures.
Constants:
- Handle infinite significant figures appropriately; usually, 3 significant figures are standard for this course.
Expectations:
- Final answers must always be reported to the correct number of significant figures. Avoid using complex significant figure tracking rules in favor of more reliable methods of class error assessment.

Key Ideas for Review:
- Units
- Base Units
- System of Units
- Dimensional Analysis
- Conversion of Units
- Order of Magnitude Estimates
- Significant Figures