Units and measurements Flashcards
What are physical quantities? How are they classified
Physical quantities are measurable properties of nature expressed in numerical values with appropriate units. They are classified into fundamental quantities (independent, e.g., length, mass, time) and derived quantities (dependent on fundamental quantities, e.g., velocity, force, energy).
What is a unit? What are the types of units
A unit is a fixed reference quantity used to measure physical quantities. There are two types: 1. Fundamental units (independent, e.g., meter, second). 2. Derived units (obtained from fundamental units, e.g., Newton = kg·m/s²).
What are the 7 fundamental quantities and their SI units
Length - Metre - m
Mass - Kilogram - Kg
Time - seconds - s
Amount of substance - Mole - mol.
Luminous intensity - Candela - cd
Temperature - Kelvin - K
Electric current - Ampere - A
What is dimensional analysis?
Dimensional analysis is the study of dimensions of physical quantities to verify equations, derive relations, and convert units. It follows the principle of homogeneity, ensuring that both sides of an equation have the same dimensions.
Limitations of dimensional analysis
- It cannot determine constants in formulas. 2. It does not work for trigonometric, logarithmic, or exponential functions. 3. It cannot verify equations with multiple terms (e.g., 𝑠 = 𝑢𝑡 + 1/2𝑎^2 cannot be derived solely by dimensions).
How do you check correctness of a formula using dimensions
Use the principle of homogeneity: Both sides of the equation must have the same dimensions. Example: Checking v = u + at. Dimensions MLT-1 = 0 + MLT-2 * T = MLT-1
Since both sides match, the equation is dimensionally correct.
What is order of magnitude? Why is it useful?
The order of magnitude of a number is the closest power of 10 that approximates it. It simplifies calculations and provides a rough estimate of large or small values. Example: For 3700, order of magnitude = 10^3.
Note: The base number has to be btn 0.5 and 5. [0.5>n<=5]
What is parallax error? How can it be minimised
Parallax error occurs when the observer’s eye is not aligned properly with the scale. It can be minimized by keeping the eye perpendicular to the scale while taking measurements.
What are supplementary units of SI
Supplementary units are radian (rad) for plane angle and steradian (sr) for solid angle. They are used in rotational motion and 3D geometry.
Convert 1 Newton to dyne
1N = 10^5 dyne
What are dimensional and dimensionless quantities?
Dimensional quantities have physical dimensions (e.g., velocity, force). Dimensionless quantities have no physical dimensions (e.g., pure numbers, angles, strain).
Dimensional variables? Examples
Dimensional variables change with time or conditions and have physical dimensions. EX: Velocity, Force, acceleration, torque
Dimensionless variables? Examples
Dimensionless variables are ratios of similar physical quantities, making their dimensions cancel out. Examples: strain, refractive index, angles
Dimensional constants? Examples
Dimensional constants have a fixed value but possess physical dimensions. Examples: Gravitational constant G, Planks constant, speed of light (c)
1 light year in metres
9.46 * 10^15
Why is the SI system preferred over other unit systems?
Universally accepted, based on fundamental constants, ensures uniformity in measurements.
Can a physical quantity have units but no dimensions? Give an example
Yes, angles (radian) and solid angles (steradian) have units but are dimensionless
Dimensions of Planks Constant
[ML^2T^-1]
Can a physical quantity have different dimensions in different unit systems?
No, dimensions remain the same across unit systems. Only unit values change.
Absolute error, relative error and percentage error
Absolute error:𝑋measured − 𝑋true
Relative error: Absolute error/True value
Percentage error: Relative error * 100
Convert 1 Horse Power into ergs per second
1HP = 746 watts = 7.46*10^9 ergs per second
Convert 1 bar or pressure into SI units (Pascal)
1 Bar = 10^5 pascal
Why does the value of the gravitational constant
G change when different unit systems are used, but the speed of light
c remains the same?
G is derived experimentally and its value depends on the unit system chosen.
c, on the other hand, is a fundamental natural constant and remains the same in all unit systems.
