Definition:Dimension (Measurement)

Definition

Every physical quantity has a dimension associated with it.

No attempt is made here to provide an abstract definition of this term. Instead, it will be defined by example.

Fundamental Dimensions

The fundamental dimensions are:

• Mass, denoted $M$ or $\mathbf M$
• Length, denoted $L$ or $\mathbf L$
• Time, denoted $T$ or $\mathbf T$

It is convenient at elementary levels of physics to add:

• Temperature, denoted $\Theta$
• Electric charge, denoted $Q$ or $\mathbf Q$

However, it is possible to define these in terms of mass, length and time, so strictly speaking they are not fundamental, as such.

Units

Compare with units of measurement.

This concept of dimension is more abstract than that of units, which are standard quantities of the particular dimension in question.

Examples

• Displacement has dimension $L$.

• Velocity has dimension $L T^{-1}$ (change in displacement, that is length traveled, per unit of time.

• Acceleration has dimension $L T^{-2}$ (change in velocity per unit of time.

• Force has dimension $M L T^{-2}$ (mass times acceleration, from Newton's Second Law.