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Questions and Answers
What is the primary purpose of measurement in physics?
What is the primary purpose of measurement in physics?
- To perform calculations without accuracy
- To quantitatively understand the natural world (correct)
- To create experimental errors
- To develop qualitative theories
Which of the following is a fundamental physical quantity?
Which of the following is a fundamental physical quantity?
- Speed
- Force
- Area
- Mass (correct)
What is a derived physical quantity?
What is a derived physical quantity?
- Volume (correct)
- Mass
- Temperature
- Time
Which unit is used for measuring length in the International System of Units (SI)?
Which unit is used for measuring length in the International System of Units (SI)?
When discussing measurement systems, which of the following refers to temperatures being measured?
When discussing measurement systems, which of the following refers to temperatures being measured?
What components are essential in defining a vector quantity?
What components are essential in defining a vector quantity?
What is an example of a physical quantity that can be measured?
What is an example of a physical quantity that can be measured?
Which of the following options represents SI prefixes?
Which of the following options represents SI prefixes?
What is the value of $z$ in the dimensional equation derived?
What is the value of $z$ in the dimensional equation derived?
What is the dimensional formula for the gravitational constant $G$?
What is the dimensional formula for the gravitational constant $G$?
Which of the following correctly balances the equation $x + z = 1$?
Which of the following correctly balances the equation $x + z = 1$?
What is the relationship between the dimensions of force, mass, and length in the formula $F = G rac{m_1 m_2}{r^2}$?
What is the relationship between the dimensions of force, mass, and length in the formula $F = G rac{m_1 m_2}{r^2}$?
Which aspect of dimensional analysis does $v = K rac{l^x m^y}{T^z}$ exemplify?
Which aspect of dimensional analysis does $v = K rac{l^x m^y}{T^z}$ exemplify?
What is the significance of negative dimensions in the dimensional equations discussed?
What is the significance of negative dimensions in the dimensional equations discussed?
What is the unit of mass per unit length represented by $
u = rac{K}{
u_ ext{actual}}$?
What is the unit of mass per unit length represented by $ u = rac{K}{ u_ ext{actual}}$?
What does the CGS system stand for?
What does the CGS system stand for?
Which statement about dimensional analysis is true according to the provided information?
Which statement about dimensional analysis is true according to the provided information?
Which of the following systems is also known by the name French system of units?
Which of the following systems is also known by the name French system of units?
What unit is defined as the mass of a platinum-iridium alloy cylinder?
What unit is defined as the mass of a platinum-iridium alloy cylinder?
Which unit measures plane angle in the International System of Units?
Which unit measures plane angle in the International System of Units?
How is the meter defined in the International System of Units?
How is the meter defined in the International System of Units?
What is a unique characteristic of dimensions in physical quantities?
What is a unique characteristic of dimensions in physical quantities?
Which of these is a fundamental unit in the International System of Units?
Which of these is a fundamental unit in the International System of Units?
What denotes the dimension of length in physical quantities?
What denotes the dimension of length in physical quantities?
What are fundamental dimensions?
What are fundamental dimensions?
Which statement best describes derived dimensions?
Which statement best describes derived dimensions?
What is the primary purpose of dimension analysis?
What is the primary purpose of dimension analysis?
What dimensions does the left-hand side (LHS) of the velocity equation $v = v_0 + at$ possess?
What dimensions does the left-hand side (LHS) of the velocity equation $v = v_0 + at$ possess?
What is the result of dimensionally analyzing the formula $E = mc^2$?
What is the result of dimensionally analyzing the formula $E = mc^2$?
Which of the following formulas represents a correct dimension analysis for wave speed?
Which of the following formulas represents a correct dimension analysis for wave speed?
In the context of dimension analysis, what does $[L][T^{-2}]$ represent?
In the context of dimension analysis, what does $[L][T^{-2}]$ represent?
Why must the dimensions of the left-hand side (LHS) and the right-hand side (RHS) of an equation be the same?
Why must the dimensions of the left-hand side (LHS) and the right-hand side (RHS) of an equation be the same?
What is the correct representation of a force vector in the xy plane?
What is the correct representation of a force vector in the xy plane?
Which of the following is a scalar quantity?
Which of the following is a scalar quantity?
What happens to the component Ax when the angle θ is 120°?
What happens to the component Ax when the angle θ is 120°?
What is the unit vector in the positive z direction denoted as?
What is the unit vector in the positive z direction denoted as?
Which equation correctly represents the resultant of vector A?
Which equation correctly represents the resultant of vector A?
What is the magnitude of a unit vector?
What is the magnitude of a unit vector?
How is a vector quantity differentiated from a scalar quantity?
How is a vector quantity differentiated from a scalar quantity?
What does the symbol 'mA' represent in electrical terms?
What does the symbol 'mA' represent in electrical terms?
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Study Notes
Physical Quantities
- A physical quantity can be measured and described by a magnitude and unit.
- Examples include: mass, length, area, temperature.
Units of Measurement
- A unit is the standard used to measure a physical quantity.
- Common systems of units include:
- CGS system: Centimetre-Gram-Second
- MKS system: Metre-Kilogram-Second
- FPS system: Foot-Pound-Second
- International System of Units (SI): the preferred system globally
International System of Units (SI)
- SI uses seven fundamental units and two supplementary units.
- Fundamental Units: Define the base quantities of the SI system.
- Length: Metre (m) - defined as the distance travelled by light in a vacuum in 1/299,792,458 of a second.
- Mass: Kilogram (kg) - defined by a platinum-iridium cylinder kept at the International Bureau of Weights and Measures.
- Time: Second (s) - defined by the time taken for 9,192,631,770 oscillations of a cesium-133 atom.
- Temperature: Kelvin (K) - the absolute temperature scale with 0 K being absolute zero.
- Electric Current: Ampere (A) - defined as the constant current that, if maintained in two straight parallel conductors of infinite length and negligible circular cross-section placed one metre apart in vacuum, would produce between these conductors a force equal to 2 x 10^-7 Newton per metre of length.
- Amount of Substance: Mole (mol) - the amount of substance that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12.
- Luminous Intensity: Candela (cd) - defined as the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 10^12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
- Supplementary Units: Refer to plane angle and solid angle.
- Plane Angle: Radian (rad) - an angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
- Solid Angle: Steradian (sr) - the solid angle subtended at the center of a sphere by its surface whose area is equal to the square of the radius of the sphere.
Dimensions
- The unique quality or type of every physical quantity that distinguishes it from all other quantities.
- Refers to the qualitative nature of a physical quantity.
- Examples:
- Length: [L]
- Mass: [M]
- Time: [T]
Fundamental and Derived Dimensions
- Fundamental Dimensions: Measured independently and constitute the essential physical quantities (e.g., Length, Mass, Time).
- Derived Dimensions: Expresses other quantities as products or quotients of fundamental dimensions (e.g., Area, Volume, Force)
Dimensional Analysis
- A method to check the correctness of a physical equation.
- All terms in an equation must have the same dimensions; if they don't, the equation is incorrect.
- Can also be used to derive physical laws.
SI Prefixes
- Used to express very large or very small quantities.
- Examples:
- milli (m): 10^-3
- micro (µ): 10^-6
- nano (n): 10^-9
- pico (p): 10^-12
- kilo (k): 10^3
- mega (M): 10^6
Vector and Scalar Quantities
- Scalar Quantities: Measured with numbers and units only.
- Examples: Length, Temperature, Time.
- Vector Quantities: Measured with numbers and units, and have a specific direction.
- Examples: Acceleration, Displacement, Force.
Components of a Vector
- Any vector can be represented by its horizontal and vertical components.
- A vector A making an angle θ with the x-axis has:
- Horizontal Component: Ax = A cosθ
- Vertical Component: Ay = A sinθ
Sign Convention for Vectors
- The signs of a vector's components depend on the quadrant it's located in.
- For example, if θ = 120°, Ax is negative and Ay is positive.
Unit Vector Notation
- A unit vector is a dimensionless vector with a magnitude of 1.
- i: unit vector in the positive x direction.
- j: unit vector in the positive y direction.
- k: unit vector in the positive z direction.
- A vector A can be expressed as:
- A = Ax i + Ay j + Az k
- Ax i is a vector of magnitude |Ax| lying on the x-axis.
- Ay j is a vector of magnitude |Ay| lying on the y-axis.
- Az k is a vector of magnitude |Az| lying on the z-axis.
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