Physical Quantities and Units

Introduction to Measurement in Physics

Physics is the study of natural phenomena, which relies heavily on measurements and equations. Every physical quantity measured in physics must have both a number and a unit. This ensures clarity and consistency in scientific communication.

• Physical Quantity: Any property of matter or energy that can be measured (e.g., mass, length, time).

• Unit: A standard quantity used to express a physical quantity (e.g., kilogram, meter, second).

• Example: Measuring the mass of a box: 5 kg (kilograms).

Physics equations require all units to be compatible with each other. Groups of compatible units form a system of units. The SI (Système International) system is the standard in physics.

Common Physical Quantities and Units

Example Equation: Force = Mass × Acceleration

Units:

Units must be compatible for equations to work correctly.

Metric Prefixes and Unit Conversion

Metric Prefixes

A metric prefix is a letter or symbol that precedes a base unit to indicate a power of ten. This allows for easy expression of very large or very small quantities.

• Example: 5 km = 5 × 103 m

• Prefixes such as kilo-, centi-, milli-, micro-, nano-, etc., represent different powers of ten.

Unit Conversion Steps

1. Identify starting and target prefixes.

2. Move from start to target, count # of exponent moves.

3. Shift decimal place in the same direction as exponent moves.

Example: Convert 6.5 hm to m.

Scientific Notation

Purpose and Format

Scientific notation is used to express very large or very small numbers in a compact form. The general format is:

• Example: Mass of Earth = kg

Converting Between Standard and Scientific Notation

Unit Conversion and Dimensional Analysis

Converting Non-SI Units

Non-SI units must be converted to SI units before using equations. This is done using conversion factors.

Steps for Converting Units

1. Write given and target units.

2. Write conversion factors/ratios.

3. Write fractions to cancel out units.

4. Multiply all factors, top and bottom, and solve.

Density and Geometric Shapes

Definition of Density

Density is defined as mass divided by volume:

Units:

Volume of Geometric Shapes

Example: Calculate the mass of Earth given its average density and radius.

Dimensional Consistency and Analysis

Dimensional Consistency

Equations in physics must be dimensionally consistent, meaning the units on both sides must match. This helps verify the correctness of equations.

• Example: Distance = speed × time () is consistent if units match.

Determining Units of Unknown Variables

Dimensional analysis is used to determine the units of unknown variables in equations.

• Example: Hooke's Law: ; units of k can be found by rearranging units.

Significant Figures and Precision

Precision in Measurements

Precision in physics is indicated by the number of digits in a measurement. More digits mean higher precision.

• Significant Figures: The digits in a measurement that carry meaning about its precision.

• Leading zeros are not significant; trailing zeros are only significant if there is a decimal point.

Counting Significant Figures

1. Eliminate leading zeros.

2. If there is a decimal, eliminate trailing zeros.

3. Count remaining digits.

4. Never eliminate non-zeros or middle zeros.

Example: 0.013200972000 has 9 significant figures.

Summary Table: Key Conversion Factors

Additional info:

• Practice problems and examples throughout the notes reinforce understanding of unit conversion, scientific notation, and dimensional analysis.

• These foundational concepts are essential for success in all areas of college-level physics.