Physics World View, Measurements, Units, and Scientific Notation

Chapter 1: A Physics World View

1. Introduction to Physics World View

Physics is the science that investigates the material world, ranging from microscopic particles to celestial bodies. The discipline seeks to uncover principles and laws governing physical phenomena, forming a shared scientific worldview that evolves as new discoveries are made.

• Physics World View: A collective body of scientific knowledge based on empirical findings.

• Dynamic Nature: The worldview changes as new ideas are proposed, tested, and either accepted or rejected.

• Criteria for Acceptance: For a theory to be adopted, it must agree with existing data and laws, and make testable predictions.

• Scientific Method: Ideas are continuously debated and tested within the scientific community.

2. Measurements & Units

Measurement is fundamental in physics, involving the comparison of a physical quantity with a standardized device. Physical quantities are classified as either fundamental or derived, and their values are always expressed with a magnitude and a unit.

• Measurement: Comparison of a physical quantity with a standard unit.

• Examples of Physical Quantities: Length, time, mass, electric current, amount of matter, temperature, light intensity.

• Expression of Measurement: Always as a number (magnitude) and a unit (e.g., L = 12 ft).

Activity Example

• Statement: "I was driving at 55 miles/hr on I-15."

• Physical Quantity: Speed

• Unit: miles/hr

• Magnitude: 55

3. Categories of Physical Quantities

Physical quantities are divided into two main categories: fundamental and derived.

• Fundamental Physical Quantities: Cannot be expressed in terms of other quantities.

• Derived Physical Quantities: Expressed in terms of fundamental quantities.

Fundamental Physical Quantities

• Length

• Time

• Mass

• Electric current

• Amount of matter

• Temperature

• Light intensity

Derived Physical Quantities

• Speed: Expressed as distance/time.

• Force: Expressed as mass × acceleration (distance/time2).

• Pressure: Expressed as force/area (mass/(distance × time2)).

4. Units and the SI System

The International System of Units (SI) provides standardized units for fundamental quantities. Prefixes are used to represent multiples or subdivisions of units for very large or small values.

• SI Units:

  • Meter (m) – length

  • Second (s) – time

  • Kilogram (kg) – mass

• Prefixes: Used for scaling units (e.g., kilo-, milli-, micro-). Additional info: Refer to SI prefix tables for full list.

• Measurement Expression: Always as a number and a unit (e.g., t = 3 d).

5. Conversion of Units

Unit conversion is often necessary in physics to express quantities in different systems. Conversion factors are used to relate units.

• Conversion Example 1: How many inches in 12 miles?

  • 1 mile = 5280 ft

  • 1 ft = 12 in

  • Calculation: $12 \times 5280 \times 12 = 760,320$ inches

• Conversion Example 2: How many feet in 8 km?

  • 1 mile = 5280 ft

  • 1.609 km = 1 mile

  • Calculation: $8 \times \frac{1}{1.609} \times 5280 = 26,252.3$ ft

6. Scientific Notation

Scientific notation is a compact way to express very large or very small numbers, commonly used in physics for convenience and clarity.

• General Form: $M \times 10^n$ where $1 \leq M < 10$ and $n$ is an integer.

• Example: The radius of a proton: $r = 0.0000000000000012$ m $= 1.2 \times 10^{-15}$ m

• Example: Earth-Moon distance: $384,000,000$ m $= 3.84 \times 10^8$ m

• Decimal Point Rule: Moving the decimal point n steps to the right subtracts n from the exponent; moving it to the left adds n.

• Example: $0.0000578 = 5.78 \times 10^{-5}$

7. Multiplying and Dividing by Powers of Ten

Operations with scientific notation follow rules for exponents.

• Multiplication: Multiply the coefficients and add the exponents.

  • Example: $2.0 \times 10^5 \times 3.0 \times 10^{-2} = 6.0 \times 10^3$

• Division: Divide the coefficients and subtract the exponents.

  • Example: $\frac{4.0 \times 10^6}{2.0 \times 10^3} = 2.0 \times 10^3$ Additional info: Example inferred for completeness.

8. Summary Table: Fundamental vs. Derived Quantities

Type	Examples	SI Unit
Fundamental	Length, Time, Mass, Electric Current, Amount of Matter, Temperature, Light Intensity	m, s, kg, A, mol, K, cd
Derived	Speed, Force, Pressure	m/s, N, Pa

9. Key Formulas

• Speed: $v = \frac{d}{t}$

• Force: $F = m \times a$

• Pressure: $P = \frac{F}{A}$