Fundamental and Derived Quantities Quiz

Study Notes

Fundamental and Derived Physical Quantities

Fundamental Physical Quantities: Independent quantities for measurement, including length, mass, time, electric current, temperature, and luminous intensity.
Derived Physical Quantities: Obtained from fundamental quantities, examples include area, volume, speed, acceleration, density, force, power, and work.

Ideal Unit Requirements

Units must be invariable, reproducible, widely available, and easy to comprehend.

Systems of Units

Fundamental Quantity Systems:
- British/F.P.S.: foot, pound, second, Fahrenheit, ampere, candela.
- C.G.S.: centimeter, gram, second, Celsius, ampere, candela.
- M.K.S.: meter, kilogram, second, Celsius, ampere, candela.
- S.I.: meter, kilogram, second, Kelvin, ampere, candela.
Unit Writing Rules: Use lowercase for unit names, avoid plural symbols, capitalize person-named units (e.g., N for Newton), and omit punctuation after symbols.

Derived Units

Units representing derived quantities include:
- Speed: L/t
- Force: MLT−2

International System of Units (SI)

Universally recognized system with basic units defined as:
- Length: Meter (m), based on a platinum-irradium standard and light travel time.
- Mass: Kilogram (kg), defined by a prototype cylinder.
- Time: Second (s), derived from the mean solar day or cesium radiation periods.
- Current: Ampere (A), defined by a specific magnetic interaction.
- Temperature: Kelvin (K), defined as 1/273.16 of the thermodynamic temperature of water's triple point.

Angular Measuring Units

Radian (rad): Measure of plane angle, defined by the radius arc it subtends.
Steradian (sr): Measure of solid angle, defined by surface area on a sphere.

Scalar and Vector Quantities

Scalar Quantities: Require only magnitude (e.g., mass, length, speed).
Vector Quantities: Require both magnitude and direction (e.g., displacement, velocity, force).

Dimensions and Dimensional Analysis

Dimensions indicate fundamental unit powers necessary to measure a physical quantity, denoted as [L], [M], [T], [A], [cd], [K].
Dimensional Formula: Represents how fundamental quantities combine to express a physical quantity. For example, area is [M° L² T°].

Error Types in Measurements

Instrumental Errors: Due to faulty instruments remaining constant through measurements.
Personal Errors: Result from setup flaws or observer mistakes.
Random Errors: Arise from unpredictable and variable experimental conditions.

Minimization of Errors

Use instruments with small least counts, take multiple measurements, and ensure significant physical quantity measurement is maximized.

True Value and Errors

Average Value: Calculated as the mean of repeated measurements.
Average Absolute Error: Average of individual errors across measurements.
Percentage Error: Ratio of average absolute error to average value, expressed in percentage.

Significant Figures

Definition: Indicates reliability in measurements, limiting one uncertain digit in a value.
Measurements should reflect precision based on the measuring device used, ensuring critical digits are accounted for.

Description

Test your understanding of fundamental and derived physical quantities in this quiz. Learn about how these quantities are measured and their significance in the physical sciences. Challenge yourself to identify and differentiate between these important concepts!