Besaran, Satuan, Dimensi, dan Pengukuran • Part 1: Besaran Pokok dan Besaran Turunan

Summary

The video introduces physical quantities, their classifications, the seven SI base quantities, and how to determine the dimensions of derived quantities.

Physical quantities and their classifications

A physical quantity is something that can be measured and expressed as a numerical value with a unit. Length and mass are examples; consumer satisfaction is not a physical quantity in this sense.

Quantities can be classified in two different ways:

• Scalar quantities have magnitude only, with no direction. Examples include length, time, and energy.
• Vector quantities have both magnitude and direction. Examples include displacement, velocity, and force. A length can be stated as “3 m,” while displacement or force also requires a direction.
• Base quantities are defined independently rather than being derived from other quantities.
• Derived quantities are formed from base quantities, such as area, speed, and force.

The seven SI base quantities

Base quantity Common quantity symbol SI unit Dimension Mass (m) kilogram (kg) ([M]) Length (l) metre (m) ([L]) Time (t) second (s) ([T]) Temperature (T) kelvin (K) ([\Theta]) Electric current (I) ampere (A) ([I]) Amount of substance (n) mole (mol) ([N]) Luminous intensity commonly (I_v) candela (cd) ([J])

Time and temperature have different dimensions: time is ([T]), while temperature is ([\Theta]). Dimensions are written using square brackets.

Determining the dimensions of a derived quantity

The dimensions of a derived quantity show which base quantities it depends on. The method is:

1. Write the quantity’s formula.
2. Replace each term with its dimension. For example, mass becomes ([M]), length becomes ([L]), and time becomes ([T]).
3. Treat constants such as (\pi) and numerical factors as dimensionless. A change symbol such as (\Delta) does not alter the dimension of the quantity.
4. Apply the formula’s multiplication and division rules. For division, subtract exponents; for powers, multiply exponents.
5. Write the final dimensions using square brackets. Negative powers can be used instead of leaving dimensions in a denominator.

Examples include:

• Area: length × length → ([L]^2)
• Volume: length × length × length → ([L]^3)
• Density: mass ÷ volume → ([M][L]^{-3})
• Speed: distance ÷ time → ([L][T]^{-1})
• Acceleration: change in velocity ÷ time → ([L][T]^{-2})
• Force: mass × acceleration → ([M][L][T]^{-2})
• Pressure: force ÷ area → ([M][L]^{-1}[T]^{-2})
• Moment of force (torque): force × distance → ([M][L]^2[T]^{-2})
• Work and energy: force × displacement, or equivalent energy formulas → ([M][L]^2[T]^{-2})
• Power: work ÷ time → ([M][L]^2[T]^{-3})
• Momentum: mass × velocity → ([M][L][T]^{-1})
• Impulse: force × time interval → ([M][L][T]^{-1})
• Moment of inertia: mass × distance squared → ([M][L]^2)

Different quantities can share the same dimensions. Work, kinetic energy, potential energy, and moment of force have the same dimensions; momentum and impulse do as well.

Dimensions and units

Dimensions and units are related, but they are not the same. Dimensions describe how a quantity depends on base quantities; units specify the standard used to measure it. For example, force has dimensions ([M][L][T]^{-2}), corresponding to the SI base units kg·m/s², which are abbreviated as newtons (N). Energy is measured in joules (J), and pressure in pascals (Pa).

Speaker and source

Christian Sutanto, presenter on the Jendela Sains channel.