Overview
This lecture introduces the foundational concepts of physics, including the nature of science, basic problem-solving steps, fundamental units, the difference between scalars and vectors, and methods for vector addition and subtraction.
Nature of Physics
- Physics is an experimental science aimed at understanding natural phenomena through observations and experiments.
- Patterns from experiments form models called physical theories.
- Well-established and widely used theories become physical laws or principles.
Problem Solving in Physics
- The four-step problem-solving strategy: Identify, Set up, Execute, Evaluate (ICSE).
- Identify relevant concepts and knowns.
- Set up by selecting appropriate equations and drawing a sketch.
- Execute the mathematics to solve.
- Evaluate the result for reasonableness.
Idealized Models
- Complex real-world objects are simplified as idealized models (e.g., treating a baseball as a point particle).
- Simplifications may omit factors like air resistance for easier analysis.
Fundamental Quantities and Units
- The three fundamental quantities: length (meter), time (second), mass (kilogram), defined by the International System (SI).
- Other unit systems: CGS (centimeter, gram, second) and British (inch, pound, mile).
- Definitions of standards:
- Second: based on cesium atom microwave frequency.
- Meter: distance light travels in vacuum in a defined fraction of a second.
- Kilogram: defined by physical constants since 2019.
Unit Prefixes and Conversions
- Prefixes indicate powers of ten (e.g., micrometer, kilometer).
- Always use consistent units in calculations and show units throughout.
- Convert units carefully using conversion factors (e.g., minutes to seconds).
Uncertainty and Significant Figures
- Uncertainty refers to the possible error in measurement; accuracy is the opposite.
- Significant figures indicate measurement precision and should be preserved in calculations.
- In multiplication/division, the result should have as many significant figures as the least precise factor.
- In addition/subtraction, the result should align with the largest uncertainty (fewest decimal places).
Scalars and Vectors
- Scalars have magnitude only (e.g., temperature, energy).
- Vectors have both magnitude and direction (e.g., displacement, force).
- Displacement is a vector defined by change in position and does not depend on path.
Vector Notation and Equality
- Vectors are denoted by arrows; their length indicates magnitude, and direction shows orientation.
- Vectors with the same magnitude and direction are equal.
- Reversing direction gives the negative of a vector.
Vector Addition and Subtraction
- Addition: Place vectors head-to-tail; order does not affect the result.
- Parallelogram method: Place tails together, complete parallelogram, and draw diagonal for resultant.
- Subtraction: Add the negative of the vector; graphically, combine head-to-head.
- Multiple vectors: Add sequentially head-to-tail or in any order; the resultant is unchanged.
Multiplying Vectors by Scalars
- Multiplying a vector by a positive scalar changes magnitude, not direction.
- Multiplying by a negative scalar changes both magnitude (by absolute value) and reverses direction.
Example: Vector Addition at Right Angles
- For perpendicular vectors, use the Pythagorean theorem for magnitude and trigonometry (tangent) for direction.
- The resultant's direction can be described relative to cardinal points (e.g., east of north).
Key Terms & Definitions
- Physics — Experimental science studying natural phenomena.
- Physical theory — Model explaining observed patterns.
- Physical law/principle — Well-established, widely used theory.
- SI Units — Standard international unit system (meter, kilogram, second).
- Scalar — Quantity with magnitude only.
- Vector — Quantity with magnitude and direction.
- Displacement — Vector showing position change.
- Significant figures — Digits reflecting measurement precision.
- Parallelogram method — Way to add two vectors graphically.
Action Items / Next Steps
- Review lecture notes and focus on understanding units, significant figures, and vector operations.
- Prepare for Thursday's continuation on vector components.
- Solve example problems on vector addition and unit conversions from the textbook.