Physical Quantities, Units, and Measurement
1. Physical Quantities and Units
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๐น Physical Quantity:
A property of a body or phenomenon that can be measured (e.g., mass, length, time).
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๐น Unit:
A standard quantity used to measure a physical quantity (e.g., metre, kilogram).
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๐น Magnitude:
The numerical value of the physical quantity when expressed in a unit.
2. SI Base Quantities and Units
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๐น Description:
Fundamental physical quantities with standard units.
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๐น Table:
Base Quantity Symbol SI Unit Unit Symbol Mass m kilogram kg Length l metre m Time t second s Electric current I ampere A Temperature T kelvin K Amount of substance n mole mol -
๐น Note:
Derived quantities (e.g., speed = m/s, force = N) are combinations of base quantities.
3. SI Prefixes
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๐น Description:
Prefixes used to simplify very large or very small quantities.
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๐น Table:
Prefix Symbol Factor nano n 10โปโน micro ฮผ 10โปโถ milli m 10โปยณ centi c 10โปยฒ deci d 10โปยน kilo k 10ยณ mega M 10โถ giga G 10โน tera T 10ยนยฒ -
๐น Tip:
1 km = 1000 m, 1 ฮผm = 10โปโถ m
4. Orders of Magnitude
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๐น Definition:
Approximate size of a quantity expressed as a power of 10.
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๐น Examples:
- ๐น Atom ~ 10โปยนโฐ m
- ๐น Human ~ 1 m
- ๐น Earth ~ 10โท m
5. Measurement
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๐น Definition:
Process of comparing a quantity with a standard unit.
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๐น Precision:
How closely repeated measurements agree.
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๐น Accuracy:
How close a measurement is to the true value.
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๐น Measuring Instruments:
- ๐น Ruler for length (cm/mm)
- ๐น Vernier caliper for precise length (0.01 cm)
- ๐น Stopwatch for time
- ๐น Balance for mass
6. Scalars and Vectors
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๐น Description:
Quantities can be scalar (magnitude only) or vector (magnitude and direction).
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๐น Table:
Type Definition Examples Scalar Quantity with magnitude only Mass, speed, temperature, energy Vector Quantity with magnitude and direction Displacement, velocity, force, acceleration -
๐น Note:
Represent vectors with arrows: length = magnitude, arrow = direction.
7. Vector Addition
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๐น Graphical Method:
- ๐น Draw the first vector to scale.
- ๐น Draw the second vector from the tip of the first vector.
- ๐น Draw the resultant from the tail of the first vector to the tip of the last vector.
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๐น Resultant Vector:
The vector that has the same effect as the combination of two or more vectors.
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๐น Mathematical Method:
Vectors can be added using components: R_x = A_x + B_x, R_y = A_y + B_y, R = โ(R_xยฒ + R_yยฒ)
- โ ๏ธ All measurements are accurate; repeated measurements may still have errors.
- โ ๏ธ Precision and accuracy are the same thing; precision relates to consistency, accuracy to correctness.
- โ ๏ธ Vectors can be added by simple arithmetic ignoring direction; direction must be considered.
- โ ๏ธ All quantities are scalars; many quantities like force and velocity are vectors.
- ๐ Memorize SI base quantities and units.
- ๐ Understand and use SI prefixes to handle large and small numbers.
- ๐ Distinguish between precision and accuracy.
- ๐ Identify scalar vs vector quantities and represent vectors graphically.
- ๐ Use vector addition methods (graphical and component-wise) correctly.