Units and Measurement
1. Physical Quantities:
Physical Quantity: A quantity that can be measured and expressed with a numerical value and unit.
Example: Length, mass, time, temperature, etc.
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2. Types of Physical Quantities:
Base Quantities: Fundamental quantities like length, mass, time.
Derived Quantities: Combinations of base quantities like velocity, force, etc.
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3. System of Units:
FPS System: Foot-Pound-Second (used in the US)
CGS System: Centimeter-Gram-Second (used for smaller physical phenomena)
MKS System: Meter-Kilogram-Second (most commonly used system globally)
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4. SI System:
The International System of Units (SI) is widely used and has seven base units:
1. Meter (m) – for length
2. Kilogram (kg) – for mass
3. Second (s) – for time
4. Ampere (A) – for electric current
5. Kelvin (K) – for temperature
6. Mole (mol) – for amount of substance
7. Candela (cd) – for luminous intensity
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5. Fundamental Dimensions:
Length (L), Mass (M), Time (T), Electric Current (I), Temperature (θ), Luminous Intensity (J), and Amount of Substance (N).
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6. Dimensional Analysis:
Process of finding relationships between physical quantities using their dimensions.
Formula: \text{Physical Quantity} = \text{Dimensional Formula} \times \text{Dimensionless Constants} ]
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7. Dimensional Formula:
Example: Velocity =
Dimension of Velocity = [L^1T^-1]
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8. Methods of Measurement:
Direct Measurement: Measuring the quantity directly (e.g., using a ruler for length).
Indirect Measurement: Using formulas to calculate a physical quantity (e.g., velocity = distance/time).
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9. Errors in Measurement:
Systematic Errors: Errors that are reproducible and occur due to faulty instruments.
Random Errors: Errors that occur randomly and have no predictable pattern.
Absolute Error: Difference between measured value and true value.
Percentage Error: \text{Percentage Error} = \left(\frac{\text{Absolute Error}}{\text{Measured Value}}\right) \times 100 ]
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10. Significant Figures:
The number of meaningful digits in a measurement.
Rules:
All non-zero digits are significant.
Zeros between two non-zero digits are significant.
Leading zeros are not significant.
Trailing zeros after a decimal point are significant.
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11. Dimensions of Physical Quantities:
[MLT]: Mass (M), Length (L), Time (T).
Example: Force = Mass × Acceleration = [M^1L^1T^-2]
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12. Conversion of Units:
Conversion from one unit to another involves multiplication or division by appropriate conversion factors.
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13. Limitations of Dimensional Analysis:
Does not provide physical explanations.
Limited to algebraic calculations.
Can only handle independent physical quantities.