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3 questions
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What do you call $ \frac{d^2 r}{dt^2}$ in polar coordinates? [duplicate]
In polar coordinates, one finds centripetal acceleration as:
$$ a_c = \frac{d^2 r}{dt^2}- \frac{v^2}{r}$$
Where $|r|$ is distance from center to particle, $v$ is tangential velocity.
My question is ...
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Terminology for time derivative of speed (not velocity)
Is there any standard terminology for the derivative of the magnitude of velocity with respect to time (suitable for use in first-year Calculus)? The word ‘acceleration’, in its technical sense, is ...
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Confusion with partial derivatives as basis vectors
So I have seen that the directional derivative can be written as
$$ \frac{df}{d\lambda} = \frac{dx^i}{d\lambda}\frac{df}{dx^i} $$
And we can identify $ \frac{d}{dx^i} $ as basis vectors and $ \...
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