Definition:Tangential Component of Acceleration

Theorem

Let $\mathbf a$ be an acceleration of a particle $P$ in space.

Let $\mathbf a$ be expressed in intrinsic coordinates as:

$\mathbf a = \dfrac {\d \map v t} {\d t} \mathbf s + \dfrac {\paren {\map v t}^2} \rho \bspsi$

where:

$\mathbf s$ denotes the unit vector along the tangential direction of $P$

$\bspsi$ denotes the unit vector toward the center of curvature of the motion of $P$

$\map v t$ is the speed of $P$ at the time $t$

$\rho$ is the radius of curvature of the motion of $P$ at time $t$

as demonstrated in Acceleration of Point in Plane in Intrinsic Coordinates.

Then the component $\dfrac {\d \map v t} {\d t} $ of $\mathbf s$ is known as the tangential component of $\mathbf a$.

Also see

• Definition:Centripetal Component of Acceleration

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): acceleration
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): tangential component
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): acceleration
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): tangential component