Fundamentals of Physics I: Representing Motion, Measurement, and Vectors

Chapter 1: Representing Motion

Introduction to Physics and Course Structure

Physics is the study of the fundamental principles governing the natural world. This course introduces students to the foundational concepts of motion, measurement, and vectors, which are essential for understanding more advanced topics in physics.

Course Materials and Assignments

• Required Materials: Scientific calculator, access to Mastering Physics, ExpertTA for labs, and the course textbook.

• Homework: Regular assignments reinforce lecture material and are crucial for learning.

• Quizzes and Exams: Weekly quizzes and three semester exams (lowest score dropped), plus a cumulative final exam.

• Collaboration: Group work and communication skills are emphasized.

Measurements, Standards, and Units

Fundamental Quantities and SI Units

Physics relies on precise measurement of fundamental quantities: length, time, and mass. The International System of Units (SI) is the standard system used worldwide.

• Length: Measured in meters (m).

• Time: Measured in seconds (s).

• Mass: Measured in kilograms (kg).

Modern Definitions of Units

• Length: Defined by the distance light travels in a vacuum in 1/299,792,458 seconds.

• Time: Defined by atomic transitions in cesium atoms.

• Mass: As of 2019, defined by the Planck constant using the Kibble balance.

Unit Prefixes and Orders of Magnitude

Prefixes are used to express larger or smaller units. Orders of magnitude help estimate and compare quantities.

• Kilo- (k): $10^3$

• Milli- (m): $10^{-3}$

• Micro- (μ): $10^{-6}$

• Nano- (n): $10^{-9}$

Accuracy, Precision, and Significant Figures

Measurement quality is described by accuracy (closeness to true value) and precision (repeatability). Significant figures indicate uncertainty.

• Multiplication/Division: Result has as many significant figures as the least precise factor.

• Addition/Subtraction: Result has as many decimal places as the least precise term.

• Exact Numbers: Do not affect significant figures.

Scientific Notation

Scientific notation simplifies writing very large or small numbers and clarifies significant figures.

• For numbers greater than 10: Move decimal left, multiply by $10^n$.

• For numbers less than 1: Move decimal right, multiply by $10^{-n}$.

Estimation and Modeling in Physics

The Estimation Tool

Estimation uses personal knowledge to build numbers in complex situations. It helps develop intuition and decide what matters in modeling.

• Use rough values and 1-digit arithmetic.

• Check answers for reasonableness.

• Order-of-magnitude estimates use the symbol $\sim$ for approximate values.

Example: Estimating Walking Speed

Estimate walking speed in meters per second using everyday experience.

• Distance: 1 mile ($\approx$ 1600 m)

• Time: 30 minutes ($\approx$ 1800 s)

• Speed: $\frac{1600\ \text{m}}{1800\ \text{s}} \approx 0.9\ \text{m/s}$

Motion: A First Look

Types of Motion and Trajectories

Motion is the change of an object's position or orientation with time. The path is called the trajectory.

Motion Diagrams and the Particle Model

Motion diagrams visually represent an object's position at successive times. The particle model simplifies objects to points for analysis.

Position, Coordinate Systems, and Time

Position is specified relative to an origin and direction. Coordinate systems use axes to mark positions. Time is labeled for each frame in a motion diagram.

Displacement and Time Intervals

• Displacement: Difference between final and initial position: $\Delta x = x_f - x_i$

• Time Interval: $\Delta t = t_f - t_i$ (always positive)

Velocity and Speed

Uniform motion is constant speed in a straight line. Speed is how fast; velocity is speed with direction.

• Average velocity: $v_{\text{avg}} = \frac{\Delta x}{\Delta t}$

• Speed: $\text{Speed} = |v|$

Scalars, Vectors, and Trigonometry

Scalars and Vectors

Scalars are quantities described by a single number and unit. Vectors have both magnitude and direction, represented by arrows.

• Magnitude: Length of the vector

• Direction: Orientation in space

Displacement Vectors

Displacement vectors show the straight-line distance and direction from initial to final position.

Adding Vectors

• Place the tail of the second vector at the tip of the first.

• Draw the resultant from the tail of the first to the tip of the second.

Vectors and Trigonometry

Trigonometry is used to calculate lengths and angles in right triangles, essential for vector analysis.

• Pythagorean theorem: $a^2 + b^2 = c^2$

• Sine: $\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}$

• Cosine: $\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

• Tangent: $\tan \theta = \frac{\text{Opposite}}{\text{Adjacent}}$

Example: Displacement Using Trigonometry

To find the net displacement when moving east then north, use the Pythagorean theorem and trigonometric ratios.

• East: 90 m, North: 50 m

• Resultant displacement: $\sqrt{90^2 + 50^2} = \sqrt{8100 + 2500} = \sqrt{10600} \approx 103$ m

• Angle: $\theta = \tan^{-1}\left(\frac{50}{90}\right) \approx 29^{\circ}$ north of east

Velocity Vectors

Velocity vectors point in the direction of motion and have magnitude equal to speed.

Summary Table: SI Base Units and Derived Units

Quantity	Unit	Symbol
Length	meter	m
Time	second	s
Mass	kilogram	kg
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

Additional info: These notes cover the foundational concepts of Chapter 1: Representing Motion, including measurement, estimation, and vector analysis, as outlined in the course syllabus for Fundamentals of Physics I.