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.