Physics 1200: Measurement, Units, Scalars, and Vectors – Study Guide

Course Structure and Policies

Instructor and Support Information

This course is taught by Dr. Michael Fellinger. Office hours are available Monday through Thursday, 1:00pm - 2:30pm, at Vernier Commons in the Physics Research Building. Additional support is provided by recitation/lab instructors and various tutoring services accessible via Carmen.

• Course documents (syllabus, policies, assignments, lecture notes) are available on Carmen under “Modules” → “Course Documents”.

• Grading is based on quizzes, midterms, final exam, prelab, labs, homework, group work, STEM fluency, and a LockDown Browser practice quiz.

• Exams and quizzes are administered online using LockDown Browser.

• Course policies are strictly enforced; exceptions are rare.

Chapter 1: Measurement and Units

Physics: Definition and Scope

Physics is the study of matter, energy, and the interactions between them. In this course, the focus is on mechanics, which examines the motion of matter and its causes.

• Kinematics: Describes how matter moves.

• Dynamics: Explains the causes of motion.

Measurement Uncertainty and Significant Figures

All measurements in physics have some degree of uncertainty. This uncertainty can be expressed in two main ways:

• Error bars: Explicitly state the possible range of error (e.g., $t = 5.0 \pm 0.1$ s).

• Significant figures: The number of reliably known digits in a measurement (e.g., $d = 1.06$ cm implies an uncertainty of $\pm 0.01$ cm).

Rules for significant figures help determine the precision of reported measurements.

SI Units and Physical Quantities

Physics uses the SI (International System of Units) for consistency and clarity. The three basic physical quantities in mechanics are:

• Mass: measured in kilograms (kg)

• Length: measured in meters (m)

• Time: measured in seconds (s)

All other physical quantities are combinations of these base units. For example:

• Speed: $\text{m/s}$

• Acceleration: $\text{m/s}^2$

• Frequency: $\text{s}^{-1}$

Non-SI units (e.g., pounds, feet, hours) may be encountered, but SI units are preferred for calculations.

Chapter 2: Scalar and Vector Quantities

Scalar Quantities

Scalars are physical quantities described completely by a single number and a unit. They do not have direction.

• Examples: length, time, temperature, mass, distance, speed

• Notation: Scalars are written using non-bold italic letters (e.g., $t$, $m$, $d$).

Vector Quantities

Vectors are physical quantities described by both a magnitude and a direction in space.

• Examples: displacement, velocity, acceleration, force

• Notation: Vectors are written using bold, non-italic letters (e.g., $\vec{x}$, $\vec{F}$) or with an arrow above the symbol.

In diagrams, vectors are represented by arrows. The direction of the arrow shows the direction of the vector, and the length of the arrow is proportional to its magnitude.

One-Dimensional Motion and Vector Direction

In one-dimensional (1D) motion, a $+$ or $-$ sign is used to indicate the direction of a vector with respect to a chosen positive direction (e.g., along the $x$-axis).

• Example: $+x$ direction is to the right on a coordinate system.

Position and Displacement

Position is the location of an object, specified by coordinates in a chosen system. The position vector points from the origin to the object's location.

• Displacement ($\Delta x$): Change in position, calculated as $\Delta x = x_2 - x_1$

• Displacement is a vector and can be positive, negative, or zero.

• Distance: Scalar quantity representing the total path length traveled (always positive).

Velocity

Velocity describes both the speed and direction of an object's motion.

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

• Instantaneous velocity: $v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}$

Average velocity considers total displacement over total time, while instantaneous velocity is the velocity at a specific moment.

Acceleration

Acceleration is the rate of change of velocity, indicating how quickly velocity changes and in which direction.

• Average acceleration: $a_{\text{avg}} = \frac{\Delta v}{\Delta t}$

• Instantaneous acceleration: $a = \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t}$

• Acceleration is a vector quantity, measured in $\text{m/s}^2$.

Equation Summary

• Displacement: $\Delta x = x_2 - x_1$

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

• Instantaneous velocity: $v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}$

• Average acceleration: $a_{\text{avg}} = \frac{\Delta v}{\Delta t}$

• Instantaneous acceleration: $a = \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t}$

Comparison Table: Scalar vs. Vector Quantities

Property	Scalar Quantity	Vector Quantity
Description	Magnitude only	Magnitude and direction
Examples	Mass, time, temperature, distance, speed	Displacement, velocity, acceleration, force
Notation	Italic letters (e.g., t, m)	Bold letters or arrow above (e.g., v, $\vec{a}$)

Key Study Tips

• Always draw diagrams and clearly label coordinate systems when solving problems.

• Pay attention to the direction and magnitude of vectors.

• Use SI units for all calculations unless otherwise specified.

• Be mindful of significant figures and measurement uncertainty.