- #36
vcsharp2003
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Yes, I get that part. If only direction of velocity is changing but not it's magnitude then tangential acceleration must be zero.haruspex said:
Yes, I get that part. If only direction of velocity is changing but not it's magnitude then tangential acceleration must be zero.haruspex said:Tangential acceleration is the component of acceleration parallel to the velocity. If speed is constant, that must be zero.
(In vectors, ##0=\frac{d}{dt}v^2=\frac{d}{dt}\vec v^2=\vec v.\dot{\vec v}=||\vec v|| a_t##.)
Why did you take derivative of ##v^2##?haruspex said:(In vectors, ##0=\frac{d}{dt}v^2=\frac{d}{dt}\vec v^2=\vec v.\dot{\vec v}=||\vec v|| a_t##.)
The speed, v, is constant if and only if ##v^2## is constant. Using the squared form let's me write it in vectors easily.vcsharp2003 said:Why did you take derivative of ##v^2##?
That's a very nice mathematical way of reasoning it, that I was unaware of. Thankyou for that great tip.haruspex said:The speed, v, is constant if and only if ##v^2## is constant. Using the squared form let's me write it in vectors easily.
But I did omit a factor 2, now corrected.