Definition:Displacement
Definition
The (physical) displacement of a body is a measure of its position relative to a given point of reference in a particular frame of reference.
Displacement is a vector quantity, so it specifies a magnitude and direction from the point of reference.
In Cartesian coordinates, the direction is implicit, as it occurs as a result of the combined distances from the various axes of the frame of reference.
Notation
When considering a displacement vector $\mathbf r$ with respect to the origin $O$ of a point $P$ in space under a Cartesian coordinate system, it is commonplace to refer to it as:
- $P = \tuple {x, y, z}$
where $x$, $y$ and $z$ are the components of $\mathbf r$ in the directions of the coordinate axes.
Hence $P = \tuple {x, y, z}$ can be regarded as shorthand for:
- $\mathbf r = x \mathbf i + y \mathbf j + z \mathbf k$
where $\mathbf i$, $\mathbf j$ and $\mathbf k$ are unit vectors along the $x$-axis, $y$-axis and $z$-axis from $O$ respectively.
Dimension
The dimension of displacement is length $\mathsf L$.
Units
SI
The SI unit of displacement is the metre.
CGS
The CGS unit of displacement is the centimetre $\mathrm {cm}$.
FPS
The FPS unit of displacement is the foot $\mathrm f$.
Also known as
The displacement of a body is also known as its position vector.
Sources
- 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Definitions: $1$.
- 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Centroids: Definition
- 1927: C.E. Weatherburn: Differential Geometry of Three Dimensions: Volume $\text { I }$ ... (next): Introduction:Vector Notation and Formulae
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{VI}$: On the Seashore
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: 1. Scalar and Vector Quantities
- 1960: M.B. Glauert: Principles of Dynamics ... (previous) ... (next): Chapter $1$: Vector Algebra: $1.1$ Definition of a Vector
- 1966: Isaac Asimov: Understanding Physics ... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $3$: The Laws of Motion: Forces and Vectors
- 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.1$ Definitions, Elementary Approach
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: displacement