- #1
Are a vector and its derivative perpendicular at all times?
- Thread starter TheCanadian
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A vector and its derivative are not always perpendicular, particularly when the vector's direction remains constant while its magnitude changes. The derivative of a vector can have both normal and tangent components. In cases where the vector's magnitude is constant, such as uniform circular motion, the derivative is indeed perpendicular. However, if the vector's magnitude increases without changing direction, the derivative points in the same direction as the original vector. Understanding these distinctions is crucial in vector calculus and physics.
- #2
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No. What if the vector is not changing direction? In general, the derivative of a vector has components both normal and tangent to the vector.
Chet
Chet
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TheCanadian said:
No. For an obvious example, consider a vector whose magnitude but not direction is increasing as a function of time: ##\vec{F}(t+\Delta{t})-\vec{F}(t)## points in the same direction as ##\vec{F}(t)##. You're thinking of the case in which the magnitude of the vector is constant over time, in which case the derivative must indeed be perpendicular (as in acceleration in the case of uniform circular motion).
[Edit: Chet got there first but I used more Latex so I still win
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