PHYS 218 Chapter 1

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Introduction

Classical (Fundamental) Mechanics

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Chapter 1: Units, Physical Quantities, and Vectors

Units

Units we'll use: meter (m), second (s), mass, (Kg)

All other units are derived from these units (e.g. 1 joule (J) = 1 kg · m²/s²)

Dimensional Analysis

$160{\frac {km}{m}}\times {\frac {1000m}{1km}}\times {\frac {39.37in}{1m}}\times {\frac {1ft}{12in}}\times {\frac {1mi}{5280ft}}=99.4mph$

Significant Figures/Digits

→ any number that is not a zero used for padding and used for accuracy:

• 3.14159 (6 sig. fig.'s)
• 3.00 &times 10⁸ (3 sig. fig.'s)
• 104,000 (3 sig. fig.'s)

Accuracy Rules

Multiplication/Division

Keep same number of sig. fig.'s as number with fewest sig. fig.'s

EX: (0.745 × 2.2) ÷ 3.885 = 0.4218… ⇒ 0.42

Addition/Subtraction

Determined by number with fewest decimal places

EX: 27.153 + 138.2 − 11.74 = 153.613 ⇒ 153.6

Vector

Recall from MATH 151 and MATH 152 Magnitude (length) and direction

Negative flips direction

All vectors are sum of components Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \hat{i}} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \hat{j}} (x and y respectively)

Recall Trigonometry with triangles: SOHCAHTOA

Example Refresher

Three players on a reality TV show are brought to the center of a large, flat field. They have to follow the following directions:

• 72.4 m, 32.0° east of north (call this A)
• 57.3 m, 36.0° south of west (call this B)
• 17.8 m, straight south (call this C)

Faster way: A + B + C = R