Units and Measurements in Physics

Study Notes

Units and Measurements

Physics relies on quantitative measurement of various physical quantities, such as mass, length, and temperature.
Measurements require a comparison with internationally accepted standard units, e.g., 5 m indicates 5 meters.
Different quantities are represented by specific units: length (meter), time (seconds), mass (kilograms).

System of Units

Fundamental quantities that do not depend on other quantities include length, mass, time, temperature, electric current, luminous intensity, and amount of substance.
Seven fundamental quantities are defined with corresponding SI units:
- Length: meter (m)
- Mass: kilogram (kg)
- Time: second (s)
- Temperature: Kelvin (K)
- Electric current: ampere (A)
- Luminous intensity: candela (cd)
- Amount of substance: mole (mol)

Measurement of Length

Standard unit for length is the meter; defined based on light's travel distance in vacuum (1983).
Large distances to celestial objects are measured using the parallax method, based on the apparent positional change due to the observer's perspective.
Common distances in meters:
- Andromeda Galaxy: 2 × 10²² m
- Proxima Centauri: 4 × 10¹⁶ m
- Pluto: 6 × 10¹² m
- Earth’s radius: 6 × 10⁶ m

Distances in Astronomy

Astronomers utilize units such as:
- 1 Astronomical Unit (AU): 1.496 × 10¹¹ m
- 1 Light Year: 9.467 × 10¹⁵ m
- 1 Parsec (pc): 3.08 × 10¹⁶ m
Angular diameter formula helps calculate the size of celestial bodies using their distance and observed angle.

Dimensional Analysis

Dimensions express derived physical quantities in terms of fundamental quantities (length, mass, time).
Equations must have same dimensions on both sides to be dimensionally correct (principle of homogeneity).
Examples of physical quantities include:
- Density: kg/m³
- Acceleration: m/s²
- Force: N (newton)

Accuracy, Precision, and Uncertainty in Measurement

Accuracy denotes how close measurements are to the true value; precision indicates reproducibility of measurements.
Uncertainties in measurements can arise from instrument quality, experimenter skill, measurement methods, and external factors.

Errors in Measurements

Errors categorized into systematic and random:
- Systematic errors arise from calibration issues or individual biases; examples include instrumental and personal errors.
- Random errors stem from unpredictable influences and can be minimized by repeated observations.

Measurement of Mass and Time

Kilogram defined by electric current as of May 20, 2019, replacing the earlier physical standard.
SI unit of time is the second (s), previously defined in relation to a solar day.

Uses of Dimensional Analysis

Checking the correctness of equations (homogeneity).
Establishing relationships between related physical quantities.
Finding conversion factors between different measurement systems.

Estimation of Error

Absolute error is the deviation of measured values from the mean; mean absolute error assesses overall measurement accuracy.
Relative error quantifies the error in relation to the mean value.

Errors in Operations

When adding or subtracting quantities, maximum absolute error is the sum of individual errors.
For products, relative error involves the sum of individual relative errors, excluding negligible products of small errors.

Description

Explore the fundamental concepts of units and measurements in physics. This quiz examines how we measure various physical quantities and the importance of standard measuring units. Test your understanding of measurement principles applicable in daily life and scientific experiments.