Study guide: Physics Foundations and Motion

📋 Course Outline

1. Physics and Its Branches
2. Scientific Methods and Variables
3. SI Quantities and Units
4. Measurement and Significant Figures
5. Conversions and Numerical Representation
6. Graphs and Relationships
7. Position and Motion
8. Motion Models and Applications

📖 1. Physics and Its Branches

🔑 Key Concepts & Definitions

• Physics: The study of matter and energy and the interactions between them.

📝 Essential Points

• Mechanics studies motion and forces, thermodynamics concerns heat, optics concerns light, and vibrations and wave phenomena include radio waves.

• Branches and their subjects include:

  • Cosmology: development and structure of the universe
  • Astrophysics: physical properties of celestial bodies
  • Nuclear physics: the atomic nucleus
  • Electromagnetism: electricity, magnetism, and their relationship

📖 2. Scientific Methods and Variables

🔑 Key Concepts & Definitions

• Hypothesis: An educated, testable explanation or prediction.
• Independent variable: The factor changed or manipulated during an investigation.
• Dependent variable: The factor in an investigation that depends on the independent variable.

★ Must-know

• A scientific investigation can proceed by observing a phenomenon, asking a question, proposing a hypothesis, testing it, analyzing results, and drawing a conclusion.

Further detail

• Ways to test a hypothesis include:
  • Experiments
  • Observations or measurements
  • Collecting and analyzing data or repeating trials

💡 Memory Hook

Observe → hypothesize → test → analyze → conclude.

📖 3. SI Quantities and Units

🔑 Key Concepts & Definitions

• Derived unit: A combination of SI base units.

★ Must-know

• The SI base units for length, mass, time, electric current, temperature, amount of substance, and luminous intensity are meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd), respectively.

Further detail

• The prefixes pico, centi, micro, and mega represent factors of 10⁻¹², 10⁻², 10⁻⁶, and 10⁶, respectively.

• The symbol Δ (delta) indicates a difference or change.

📖 4. Measurement and Significant Figures

🔑 Key Concepts & Definitions

• Accuracy: How closely a measured value agrees with the accepted value.
• Precision: How closely repeated measurements agree with one another.

📝 Essential Points

• Rachel's density measurements of 11.32, 11.35, and 11.33 g/cm³ are both accurate and precise relative to the accepted value of 11.34 g/cm³.

📌 Daniel's density measurements of 11.43, 11.44, and 11.42 g/cm³ are precise but not accurate relative to the accepted value of 11.34 g/cm³.

• Leah's density measurements of 11.55, 11.34, and 11.04 g/cm³ are not precise because they vary widely, even though one equals the accepted value of 11.34 g/cm³.

💡 Memory Hook

Accuracy is closeness to the accepted value; precision is closeness among repeated measurements.

📖 5. Conversions and Numerical Representation

★ Must-know

• Scientific notation expresses a number as a coefficient multiplied by a power of ten, with the coefficient written between 1 and 10 in magnitude.

📌 For multiplication and division, round the result to the same number of significant figures as the input with the fewest significant figures.

📌 For addition and subtraction, round the result to the least precise decimal place among the inputs.

Further detail

• The measurement 702.0 g written in scientific notation is 7.020 × 10² g and has four significant figures.

• The measurement 20.070 km contains five significant figures.

• Dimensional analysis converts units by multiplying a quantity by conversion factors that preserve its value while changing its units.

• Seven years contain 61,320 hours when each year is taken as 365 days.

• A speed of 35 km/h is equivalent to 972 cm/s.

📖 6. Graphs and Relationships

🔑 Key Concepts & Definitions

• Line of best fit: A line that describes data and predicts where new data points may appear on a graph.

★ Must-know

• A linear relationship is represented by a straight-line graph and can be written as $y = mx + b$.

• A quadratic relationship can be written as $y = ax^2 + bx + c$ and produces a parabolic graph.

Further detail

• An inverse relationship can be represented by $y = \frac{a}{x}$.

• For a mass on a nearly frictionless table measured over 5 seconds, distance in centimeters relates to applied force in newtons as $d = 5F$, so the proportionality constant is 5 cm/N.

• For a spring with initial length 48 cm and slope 0.16 cm/g, its length L in centimeters varies with attached mass m in grams as $L = 0.16m + 48$.

📖 7. Position and Motion

🔑 Key Concepts & Definitions

• Position: An object's location relative to a reference point.
• Distance: The total length of the path traveled; a scalar quantity.
• Displacement: The change in position from an initial point to a final point; a vector with direction.
• Motion diagram: A series of images that records a moving object's position at equal time intervals.
• Coordinate system: A system specifying a zero point and the direction in which the variable's values increase to describe motion.

📝 Essential Points

📐 Formula - The time interval is the difference between final and initial times: $\Delta t = t_f - t_i$.

💡 Memory Hook

Distance totals the path; displacement compares final and initial positions.

📖 8. Motion Models and Applications

★ Must-know

📐 Formula - For a falling object near Earth's surface, Galileo's distance relation is $d = \frac{1}{2}gt^2$, where g is approximately 9.8 N/kg toward Earth's center.

📐 Formula - For a constant force, the data show acceleration inversely proportional to mass, approximately $a = \frac{12}{m}$, where the constant is about 12 N.

Further detail

📌 In Galileo's falling-object relation, time is the independent variable and distance is the dependent variable because distance changes as time changes.

• Because falling distance is proportional to the square of time, its graph against time is parabolic rather than linear.

• For a coach moving from initial position 70 m to final position −20 m, displacement is −90 m, or 90 m to the left, while the total traveled distance is 150 m.

• A van traveling 6.0 km east, then 8.0 km west, then 6.0 km west covers 20.0 km and has a net displacement of 8.0 km west.

💡 Memory Hook

At constant force, increasing mass causes acceleration to decrease.

📊 Synthesis Tables

Position, Distance, and Displacement

Quantity	Meaning	Type
Position	Location relative to a reference point	Location
Distance	Total length of the path traveled	Scalar
Displacement	Change from initial to final position	Vector with direction

Linear and Nonlinear Relationships

Relationship	Equation	Graph shape
Linear	y = mx + b	Straight line
Quadratic	y = ax² + bx + c	Parabola
Inverse	y = a/x	Inverse curve