Podcast
Questions and Answers
Which of the following is an example of a fundamental physical quantity?
Which of the following is an example of a fundamental physical quantity?
- Volume
- Force
- Mass (correct)
- Area
Derived units are combinations of fundamental units.
Derived units are combinations of fundamental units.
True (A)
What is the purpose of measurement in the context of physical quantities?
What is the purpose of measurement in the context of physical quantities?
to compare a physical quantity with an internationally accepted value.
In the CGS system, length is measured in _______.
In the CGS system, length is measured in _______.
Match the unit system with its base units for length, mass, and time:
Match the unit system with its base units for length, mass, and time:
What is the key feature of the SI unit system?
What is the key feature of the SI unit system?
Units conversion is unnecessary when dealing with different scales of measurement.
Units conversion is unnecessary when dealing with different scales of measurement.
Why is it important to convert units from kilometers to centimeters when measuring the length of a pencil?
Why is it important to convert units from kilometers to centimeters when measuring the length of a pencil?
When converting from a smaller unit to a larger unit, one must use _______ conversion factors.
When converting from a smaller unit to a larger unit, one must use _______ conversion factors.
Match the length unit conversions:
Match the length unit conversions:
What does dimensional analysis primarily deal with?
What does dimensional analysis primarily deal with?
Dimensional analysis is purely theoretical and has no practical use in experimental work.
Dimensional analysis is purely theoretical and has no practical use in experimental work.
Give an example of a fundamental dimension.
Give an example of a fundamental dimension.
The dimension of density is denoted by _______.
The dimension of density is denoted by _______.
Match the derived quantity with its dimensional formula:
Match the derived quantity with its dimensional formula:
What is the dimension of a dimensionless quantity?
What is the dimension of a dimensionless quantity?
According to the rules of dimensional analysis, physical quantities with different dimensions can always be added together.
According to the rules of dimensional analysis, physical quantities with different dimensions can always be added together.
Give an example of a non-algebraic function.
Give an example of a non-algebraic function.
The dimensional formula for energy is ______.
The dimensional formula for energy is ______.
Match the value of mass of proton, Earth's mass, Boltzmann constant:
Match the value of mass of proton, Earth's mass, Boltzmann constant:
Which base quantity and SI unit pair is correctly matched?
Which base quantity and SI unit pair is correctly matched?
According to base quantities, the SI symbol of temperature is degree Celcius.
According to base quantities, the SI symbol of temperature is degree Celcius.
A room's area is best expressed in which unit?
A room's area is best expressed in which unit?
The numbers or constants does not have ______.
The numbers or constants does not have ______.
Match the following power of ten with unit:
Match the following power of ten with unit:
Which of the following represents the dimensional formula of Pressure?
Which of the following represents the dimensional formula of Pressure?
In dimensional analysis, physical formulas can be derived by setting dimensional equations for involved quantities.
In dimensional analysis, physical formulas can be derived by setting dimensional equations for involved quantities.
In dimensional analysis, what role does assuming a power-law relationship play?
In dimensional analysis, what role does assuming a power-law relationship play?
If we claim that $T = k \sqrt{\frac{l}{g}}$, what does g stand for?
If we claim that $T = k \sqrt{\frac{l}{g}}$, what does g stand for?
Match the unit conversion:
Match the unit conversion:
When the number of unit changes, will it has effect on the physical quantity?
When the number of unit changes, will it has effect on the physical quantity?
Since velocity, density and acceleration involve more than one fundamental quantities so these are not called derived quantities.
Since velocity, density and acceleration involve more than one fundamental quantities so these are not called derived quantities.
What is the dimensional formula for area?
What is the dimensional formula for area?
The SI unit for temperature is ______.
The SI unit for temperature is ______.
Match the volume conversion:
Match the volume conversion:
The dimension for force is:
The dimension for force is:
The dimension of a dimensionless quantity is zero.
The dimension of a dimensionless quantity is zero.
For a gas bubble, in what terms is statis preasure (P) presented in dimensionally?
For a gas bubble, in what terms is statis preasure (P) presented in dimensionally?
In dimensional analysis quantities M, L and T represents for ______, length and time respectively.
In dimensional analysis quantities M, L and T represents for ______, length and time respectively.
Match the values:
Match the values:
Flashcards
Physical Quantities
Physical Quantities
Quantities that can be measured and describe physical phenomena.
Fundamental Quantities
Fundamental Quantities
Quantities independent of others (Mass, Length, Time).
Fundamental Units
Fundamental Units
Units for fundamental quantities (length, time).
Derived Units
Derived Units
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Units
Units
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CGS System
CGS System
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FPS System
FPS System
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MKS System
MKS System
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SI Unit System
SI Unit System
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Dimensional Analysis
Dimensional Analysis
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Fundamental Dimensions
Fundamental Dimensions
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Derived Dimensions
Derived Dimensions
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Dimensionless Quantity
Dimensionless Quantity
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Elastic properties
Elastic properties
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Study Notes
Units and Dimensions: Principles of Physics
- This document covers fundamental and derived physical quantities, unit systems, unit conversions, dimensional analysis and their uses in physics.
Physical Quantities and Their Types
- Physical quantities are measurable and necessary to describe physical phenomena.
- Fundamental physical quantities are independent and don't depend on other quantities, while examples are mass, length, and time.
- Derived physical quantities can be expressed in terms of fundamental physical quantities, such as area, volume, force, work and pressure.
Measurement and Unit Systems
- Measurement involves comparing a physical quantity to an internationally accepted value.
- A unit is an internationally accepted standard value for measurements.
- Fundamental units: Units for fundamental or base quantities like length and time.
- Derived units are combinations of base units
- Speed measured as distance/time is measured in meters per second (m/s).
- Acceleration measured as change in velocity/time is measured in meters per second squared (m/s²).
- Force measured as mass x acceleration is measured in kilogram meters per second squared (kg m/s²).
- Energy measured as force x distance is measured in kilogram meters squared per second squared (kg m²/s²), equivalent to Newton-meters (Nm) or Joules (J).
Types of Unit Systems
- CGS system uses centimeter, gram, and second as base units.
- FPS system uses foot, pound, and second as base units.
- MKS system uses meter, kilogram, and second as base units.
- The MKS unit of force is the Newton, while the CGS unit is the dyne.
- The MKS unit of work/energy is the Joule, while the CGS unit is the erg.
- Conversions
- 1 foot equals 30.48 cm.
- 1 hour equals 3600 seconds.
- 1 pound equals 454 grams.
- 1 Newton equals 105 dynes.
- 1 joule equals 107 ergs.
- 9.8 m/s² equals 980 cm/s².
- SI unit system: It is the Système Internationale d' Unites or the International System of Units and was developed and recommended by the General Conference on Weights and Measures in 1971. Length is measured in meters (m), mass in kilograms (kg), time in seconds (s), electric current in Amperes (A or I), temperature in Kelvin (K), luminous intensity in candelas (cd), and amount of substance in moles (mol)
Units Conversion
- The appropriate unit depends on the situation; area of a room is expressed in meters while the length of a pencil is expressed in centimeters
- Accuracy and clarity requires converting between units.
- Unit conversion is performed using multiplicative conversion factors.
- Common Conversions and Symbols
Dimensional Analysis
- Dimensional analysis is a mathematical technique to study dimensions
- It is used for research design and model testing, dealing with the dimensions of physical quantities, measured against a fixed value.
- Dimensional analysis helps predict physical parameters, group them in dimensionless combinations, and guide experimental work to influence phenomena.
Types of Dimensions
- There exist fundamental and secondary dimensions
- Fundamental dimensions are basic quantities like time (T), distance (L), and mass (M).
- Secondary dimensions possess more than one fundamental dimension
- Denoted by distance per unit time (L/T)
- Acceleration is denoted by distance per unit time squared (L/T²), and density is denoted by mass per unit volume (M/L³).
- Quantities involving more than one fundamental quantity are derived quantities.
Dimensional Analysis
- The document provides lists of physical quantities with their dimensional formulas.
- Physical Dimensional Constants such as the Speed of Light, Mass of Proton, etc.
Important rules
- Any required dimension for physical quantity analysis needs to be expressed in terms of mass (M), length (L), and time (T).
- When writing out a dimension, order should be observed
- Multiplication and division of dimensions is possible
- Addition and subtraction of dimensions is not possible
- Two quantities A and B cannot be added or subtracted if their units of measure are different.
- Two quantities A & B can be multiplied or divided
Dimensionless Quantity
- Refer to all the numbers that are dimensionless
- Refers to any constant (such as π = 22/7 = 3.14) that is dimensionless
- All ratios are dimensionless
- All non-algebraic functions are dimensionless
- Such as logarithmic functions log(x), ln(x) Exponential Functions ex, ax
- Trigonometric Functions sin(x), cos(x), tan(x)
- The dimension of a dimensionless quantity is 1
Verifying Equations
- Dimensional analysis can verify the correctness of equations
- It involves confirming that the dimensions on both sides of an equation are consistent.
Deducing Laws
- Dimensional analysis can deduce a law to find relationships between physical quantities by analyzing their dimensions
Examples
- Several worked examples of unit conversions are provided.
- Also calculating dimensions of the equations using dimensional analysis
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