Introduction to Motion: Study Notes for Calculus-Based Physics

Welcome and Introduction to Motion

Course Overview

This course is a first-semester, calculus-based physics class designed for science and engineering majors. It emphasizes foundational concepts in motion, vectors, and mathematical modeling, preparing students for advanced topics in physics.

• Target Audience: Science and engineering students

• Prerequisites: Familiarity with calculus, especially derivatives

• Textbook: Physics for Scientists and Engineers by Randall Knight (5th Edition)

Big Ideas in Motion

Particle Model and Motion Diagrams

The particle model simplifies objects to single points to analyze their motion. Motion diagrams visually represent the position of an object at regular time intervals, helping to understand concepts like velocity and acceleration.

• Particle Model: Treats objects as points to focus on their movement rather than their size or shape.

• Motion Diagram: Sequence of dots showing an object's position at equal time intervals.

• Sign Conventions: Positive and negative directions must be defined for consistent analysis.

Example: A sled moving down a hill can be represented by a series of dots spaced at regular intervals, indicating its changing position over time.

Position, Displacement, and Velocity

Position is the location of an object at a particular time. Displacement is the change in position, and velocity describes both the speed and direction of motion.

• Position (x, y): Measured in meters (m) using a coordinate system.

• Displacement (Δx): The vector difference between final and initial positions.

• Velocity (v): Rate of change of position; a vector quantity.

Formula:

• Displacement: $\Delta x = x_{\text{final}} - x_{\text{initial}}$

• Average Velocity: $\vec{v}_{\text{avg}} = \frac{\Delta \vec{x}}{\Delta t}$

Example: If an ant moves back and forth on a picnic table, its total displacement is the straight-line distance from its starting to ending position, while the total distance traveled is the sum of all segments.

Vectors and Scalars

Vectors have both magnitude and direction, while scalars have only magnitude. Vectors are represented by arrows, and their length indicates magnitude.

• Vector Addition: Place the tail of one vector at the head of another (tip-to-tail method).

• Vector Subtraction: Add the negative of the vector to be subtracted.

• Scalar Quantity: Only has size (e.g., mass, temperature).

Example: Displacement and velocity are vectors; distance and speed are scalars.

Speed and Velocity

Speed is the rate at which an object covers distance, while velocity includes direction.

• Average Speed: $\text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Spent Traveling}}$

• Average Velocity: $\vec{v}_{\text{avg}} = \frac{\Delta \vec{x}}{\Delta t}$

Example: A runner moving along a straight track at constant velocity will have equal spacing between positions in a motion diagram.

Scientific Notation and SI Units

Scientific Notation

Scientific notation is used to express very large or very small numbers efficiently. Move the decimal point until only one nonzero digit remains to the left, and count the steps to determine the exponent.

• Example: $6,370,000\,\text{m} = 6.37 \times 10^6\,\text{m}$

• Example: $0.0000075\,\text{m} = 7.5 \times 10^{-6}\,\text{m}$

SI Units and Prefixes

The International System of Units (SI) uses base units and prefixes to represent quantities.

• Length: meter (m)

• Mass: kilogram (kg)

• Time: second (s)

• Common Prefixes:

Prefix	Symbol	Factor
milli	m	$10^{-3}$
micro	μ	$10^{-6}$
nano	n	$10^{-9}$
pico	p	$10^{-12}$

Example: 100 centimeters (cm) = 1 meter (m)

Academic Integrity and Success Strategies

Academic Integrity

Maintaining academic honesty is essential. Plagiarism and other forms of misconduct are strictly prohibited and subject to university policy.

• Never submit someone else's work as your own.

• Refer to the CSU General Catalog for details.

Success Strategies

Engagement with course materials and collaboration with peers are strongly correlated with success in introductory physics.

• Read the textbook before class.

• Practice sample problems.

• Work with classmates.

• Attend office hours and recitations.

Additional info: The course uses low-tech clickers for in-class participation and encourages active learning through group work and discussions.