Understanding Base Units in Physics

In physics and measurement, units are categorized into base units and derived units. Base units are a set of fundamental units from which all other units can be derived. The International System of Units (SI) defines seven base units. Understanding these base units is crucial for comprehending various physical quantities and their measurements.

Identifying the SI Base Units

The seven fundamental SI base units are:

• Meter (m) for length
• Kilogram (kg) for mass
• Second (s) for time
• Ampere (A) for electric current
• Kelvin (K) for thermodynamic temperature
• Mole (mol) for amount of substance
• Candela (cd) for luminous intensity

Analyzing the Given Options

The question asks which of the given options is NOT a base unit. Let's examine each option in relation to the list of SI base units:

• mole: The mole (mol) is the SI base unit for the amount of substance.
• ampere: The ampere (A) is the SI base unit for electric current.
• radian: The radian (rad) is a unit for measuring angles. While fundamental in geometry, it is considered a derived unit in the SI system (specifically, a dimensionless derived unit).
• candela: The candela (cd) is the SI base unit for luminous intensity.

Determining the Unit That is NOT a Base Unit

Based on the definition of SI base units and our analysis of the options, the units mole, ampere, and candela are all included in the list of the seven fundamental SI base units. The radian, however, is a unit used for plane angles and is classified as a derived unit within the SI system, even though it is dimensionless.

Therefore, the unit that is NOT a base unit among the given options is the radian.

Conclusion

The question asks to identify the unit that is NOT a base unit. From the options provided, mole, ampere, and candela are SI base units. Radian is a derived unit for plane angles. Hence, radian is the correct answer.

Revision Table: Key SI Units

Additional Information: Derived Units vs. Base Units

Derived units are units that are combinations of base units. For example, the unit for speed, meters per second (m/s), is derived from the base units of length (meter) and time (second). The unit for force, Newton (N), is derived from kilograms, meters, and seconds (\[\text{N} = \text{kg} \cdot \text{m}/\text{s}^2\]).

Radian is a special type of derived unit. It is a unit for plane angle, defined as the ratio of the arc length subtending the angle to the radius of the circle. Since it is a ratio of two lengths, it is dimensionless. The steradian (sr) is the SI derived unit for solid angle, and it is also dimensionless. While sometimes referred to as "supplementary units" historically, the SI currently classifies radian and steradian as derived units.