Vector Quantity/Examples

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Examples of Vector Quantities

Displacement

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.


Velocity

The velocity $\mathbf v$ of a body $M$ is defined as the first derivative of the displacement $\mathbf s$ of $M$ from a given point of reference with respect to time $t$:

$\mathbf v = \dfrac {\d \mathbf s} {\d t}$


Acceleration

The acceleration $\mathbf a$ of a body $M$ is defined as the first derivative of the velocity $\mathbf v$ of $M$ relative to a given point of reference with respect to time $t$:

$\mathbf a = \dfrac {\d \mathbf v} {\d t}$


Linear Momentum

The linear momentum of a body is its mass multiplied by its velocity.

$\mathbf p = m \mathbf v$


Angular Momentum

Let $P$ be a particle of mass $m$ moving with velocity $\mathbf v$ relative to a point $O$.

The angular momentum of $P$ relative to (or about) $O$ is defined as:

$\mathbf L = \mathbf r \times \mathbf p = m \paren {\mathbf r \times \mathbf v}$

where:

$\mathbf p$ denotes the (linear) momentum of $P$
$\mathbf r$ denotes the position vector of $P$ with respect to $O$
$\times$ denotes the vector cross product.