Lateral speed

Transverse speed ( transverse speed , azimuthal speed ) - the projection of the speed of a point (in the figure - A) on a straight line, perpendicular to the radius vector ${\vec {OA}}.$ ${\ displaystyle {\ vec {OA}}.}$ ${\ vec {OA}}.$

In cylindrical (and polar ) and spherical coordinate systems, one of the velocity components (the other component is the radial (radial) velocity ). Thus, it is the generalized velocity in these coordinate systems.

By definition, the azimuthal velocity is a scalar and is found by the formula:

$v_{\phi }={\vec {v}}\cdot {\vec {e}}_{\phi }$ ${\ displaystyle v _ {\ phi} = {\ vec {v}} \ cdot {\ vec {e}} _ {\ phi}}$ $v _ {\ phi} = {\ vec {v}} \ cdot {\ vec {e}} _ {\ phi}$ ,

Where ${\vec {e}}_{\phi }={\frac {\partial {\vec {r}}}{\partial \phi }}$ ${\ displaystyle {\ vec {e}} _ {\ phi} = {\ frac {\ partial {\ vec {r}}} {\ partial \ phi}}}$ ${\ vec {e}} _ {\ phi} = {\ frac {\ partial {\ vec {r}}} {\ partial \ phi}}$ - unit directed along the coordinate $\phi$ ${\ displaystyle \ phi}$ $\ phi$ .

The azimuthal velocity expressed in coordinates is

$v_{\phi }=r{\frac {d\phi }{dt}}=r{\dot {\phi }}$ ${\ displaystyle v _ {\ phi} = r {\ frac {d \ phi} {dt}} = r {\ dot {\ phi}}}$ $v _ {\ phi} = r {\ frac {d \ phi} {dt}} = r {\ dot {\ phi}}$

Lateral speed

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