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 ${\hat {i}}$ and ${\hat {j}}$ (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