Dimension

Definition

A dimension is a measurable extent of some kind, such as length, time, or mass. In physics, dimensions are used to quantify physical quantities and describe their dependence on fundamental units.

5 Must Know Facts For Your Next Test

1. There are seven fundamental dimensions in the International System of Units (SI): length (L), mass (M), time (T), electric current (I), thermodynamic temperature ($\Theta$), amount of substance (N), and luminous intensity (J).
2. Dimensional analysis involves checking the consistency of dimensions in equations and converting between different units.
3. Using dimensional analysis can help deduce relationships between physical quantities without detailed knowledge of the underlying phenomena.
4. Physically meaningful equations must be dimensionally homogeneous, meaning all terms must have the same dimensional formula.
5. The Buckingham π theorem is a key principle in dimensional analysis, stating that any physically meaningful equation involving n variables can be reduced to a relationship among n - k dimensionless parameters, where k is the number of fundamental dimensions.

Review Questions

• What are the seven fundamental dimensions in the SI system?
• Why must equations be dimensionally homogeneous?
• How does the Buckingham π theorem assist in simplifying complex physical relationships?

Related terms

Unit: A standard quantity used to specify measurements. Examples include meters for length and seconds for time.

Dimensional Homogeneity: A property of an equation wherein all terms have the same dimensional formula, ensuring it is physically meaningful.

Buckingham π Theorem: A key principle in dimensional analysis that allows reduction of complex physical problems to simpler forms using dimensionless parameters.