Definition:Centripetal Component of Acceleration
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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 $t$.
Then the component $\dfrac {\paren {\map v t}^2} \rho$ of $\bspsi$ is known as the centripetal component of $\mathbf a$.
Also known as
The centripetal component of acceleration is also known as the normal component
Also see
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): centripetal 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): centripetal component