Introduction to Units and the S.I. System

Understanding Physical Quantities and Units

• Physics is the study of natural phenomena, which includes the use of measurements and equations. To describe the physical world, we use physical quantities (such as mass, length, and time) that must be measured using standard units. The International System of Units (S.I.) is the globally accepted system for these measurements.

  • Physical Quantity: A property of a material or system that can be quantified by measurement (e.g., mass, length, time).

  • Unit: A standard quantity used to specify measurements (e.g., kilogram for mass, meter for length, second for time).

  • All units in a physics equation must be compatible for the equation to be valid.

Example: The equation for force is (Force = Mass × Acceleration). The units must be compatible: .

Metric Prefixes

Using Prefixes to Express Large and Small Quantities

Metric prefixes are used to express very large or very small quantities by attaching a prefix to the base unit. Each prefix represents a specific power of ten.

• Kilo- (k):

• Centi- (c):

• Milli- (m):

• Micro- (μ):

• Nano- (n):

Example: ,

When converting between units with prefixes, shifting from a bigger to a smaller unit increases the number, and vice versa.

Scientific Notation

Expressing Very Large or Small Numbers

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

• Standard Form to Scientific Notation: Move the decimal point to create a number between 1 and 10, and count the number of places moved as the exponent.

• Scientific Notation to Standard Form: Move the decimal point according to the exponent.

Example:

Unit Conversions

Converting Between Different Units

Unit conversions are essential in physics to ensure all quantities are in compatible units. Conversion factors are used to change from one unit to another.

Example: To convert 22 lbs to kg:

Solving Density Problems

Calculating Density, Mass, and Volume

Density is defined as mass divided by volume:

• For a rectangular solid:

• For a sphere:

• For a cylinder:

Example: If a wooden cylinder has a radius of 1.5 cm, height of 6 cm, and mass of 18 g, its density is

Dimensional Analysis

Checking Consistency and Determining Units

Dimensional analysis is used to check if equations are dimensionally consistent and to determine the units of unknown variables.

• Equations are valid only if both sides have the same dimensions.

• Units can be treated algebraically to solve for unknowns.

Example: For , the units of can be found by rearranging the equation and substituting the units for force, mass, and distance.

Significant Figures

Precision in Measurements and Calculations

Significant figures (sig figs) indicate the precision of a measurement. The number of significant digits reflects the certainty of the measurement.

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant; trailing zeros in a decimal are significant.

Example: 0.013200972 has 8 significant figures.

Rules for Calculations with Significant Figures

• Addition/Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.

• Multiplication/Division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

Example: (2 sig figs)

Summary Table: Common SI Units and Prefixes

Additional info: These foundational concepts are essential for all subsequent topics in physics, as they ensure clarity, consistency, and accuracy in scientific communication and problem-solving.