Chapter 1: Concepts of Motion – PHYSICS 1051 Study Notes

Chapter 1: Concepts of Motion

Introduction to Motion

Understanding motion is fundamental to physics, as it allows us to describe and predict the behavior of objects in our universe. The study of motion begins with philosophical questions and paradoxes, such as those posed by Zeno and Diogenes, and progresses to precise scientific definitions and measurements.

• Motion: The change in position of an object relative to a reference point.

• Reference Point: A fixed location from which distances are measured.

• Philosophical Context: Zeno's paradoxes challenge the concept of motion, while Diogenes provides practical counterarguments.

Zeno's Dichotomy Paradox

Zeno of Citium proposed paradoxes questioning the reality of motion. The Dichotomy Paradox states that to reach a destination, one must first reach halfway, then a quarter, an eighth, and so on, requiring an infinite number of steps.

• Infinite Tasks: The paradox suggests motion is impossible due to infinite subdivisions.

• Resolution: Modern mathematics resolves this with the concept of convergent series.

Motion Diagrams

Motion diagrams visually represent the position of an object at successive time intervals, helping to analyze its movement.

• Video Analysis: Images taken at a fixed rate (e.g., 30 frames/second) show the object's position over time.

• Constant Speed: Equal spacing between positions indicates constant speed.

• Speed: The rate of change of position, measured in meters per second (m/s).

Scalars and Vectors

Physical quantities are classified as scalars or vectors.

• Scalars: Have only magnitude (e.g., speed).

• Vectors: Have both magnitude and direction (e.g., velocity, acceleration).

• Representation: Vectors are depicted by arrows; the length indicates magnitude, and the direction shows orientation.

Velocity and Acceleration

Velocity and acceleration are key concepts in describing motion.

• Velocity (v): Rate of change of position vector, measured in m/s.

• Acceleration (a): Rate of change of velocity, measured in m/s2.

Formulas:

• Average velocity: $\vec{v}_{avg} = \frac{\Delta \vec{r}}{\Delta t}$

• Average acceleration: $\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}$

Speeding Up or Slowing Down

Whether an object speeds up or slows down depends on the direction of the acceleration vector relative to the velocity vector.

• Parallel Acceleration: Acceleration in the same direction as velocity increases speed.

• Anti-parallel Acceleration: Acceleration in the opposite direction decreases speed.

• Perpendicular Acceleration: Changes the direction of velocity without changing speed (e.g., circular motion).

Position Vector

The position vector specifies the location of a point relative to the origin.

• Components: In two dimensions, position is given by x and y coordinates.

• Magnitude: The distance from the origin to the point.

• Displacement: Change in position, represented by $\Delta \vec{r}$.

Displacement and Time Intervals

Displacement and time intervals are essential for calculating velocity and acceleration.

• Displacement: $\Delta \vec{r} = \vec{r}_f - \vec{r}_i$

• Time Interval: $\Delta t = t_f - t_i$

• Invariance: All observers agree on displacement and time intervals, regardless of reference point.

Types of Motion

Motion can be classified as linear, circular, projectile, or rotational.

• Linear Motion: Movement along a straight line.

• Circular Motion: Movement along a circular path; speed can be constant while acceleration is non-zero.

• Projectile Motion: Motion under the influence of gravity.

• Rotational Motion: Rotation around an axis.

Units and Measurements

Physics relies on precise measurements using standardized units.

• SI Units: The International System of Units includes the meter (m), kilogram (kg), and second (s).

• Time: Defined by the oscillations of a cesium-133 atom.

• Length: Defined by the distance light travels in a vacuum in a specified fraction of a second.

• Mass: Defined by Planck's constant.

Common SI Prefixes

Prefix	Power of 10	Abbreviation
giga-	109	G
mega-	106	M
kilo-	103	k
centi-	10-2	c
milli-	10-3	m
micro-	10-6	μ
nano-	10-9	n

Unit Conversion

Converting between units is essential for solving physics problems.

• Use conversion factors as ratios equal to one.

• Example: $1 \text{ in} = 2.54 \text{ cm}$, $1 \text{ mi} = 1.609 \text{ km}$

Unit	Equivalent
1 in	2.54 cm
1 mi	1.609 km
1 mph	0.447 m/s
1 m	39.37 in
1 km	0.621 mi
1 m/s	2.24 mph

Significant Figures

Significant figures communicate the precision of measurements and calculations.

• Definition: The digits in a measurement that are known with certainty plus one estimated digit.

• Rules:

  • Multiplication/Division/Roots: Use the least number of significant figures from the input values.

  • Addition/Subtraction: Use the least number of decimal places.

• Example: 6.2 has two significant figures; 6.20 has three.

Orders of Magnitude

Order-of-magnitude estimates provide approximate values, useful for quick calculations and comparisons.

• Symbol: $\sim$ indicates an estimate with one significant figure.

• Application: Estimating the speed of a falling rock as $v \sim 20$ mph.

Summary Table: Key Concepts

Concept	Definition	Unit
Speed	Distance per unit time	m/s
Velocity	Speed with direction	m/s
Acceleration	Change in velocity per unit time	m/s2
Displacement	Change in position	m
SI Units	Standard units for measurement	m, kg, s

Additional info: These notes are based on introductory lecture slides for Physics 1051, focusing on the foundational concepts of motion, measurement, and scientific precision. They are suitable for exam preparation and review of core principles in college-level physics.