A formula that calculates from B and v If we start with
Chapter 12, Problem 28E(choose chapter or problem)
A formula that calculates \(\tau\) from B and v If we start with the definition \(\tau=-(d B / d s) \cdot N\) and apply the Chain Rule to rewrite \(d B / d s\) as
\(\frac{d B}{d s}=\frac{d B}{d t} \frac{d t}{d s}=\frac{d B}{d t} \frac{1}{|v|}\)
we arrive at the formula
\(\tau=-\frac{1}{|v|}\left(\frac{d B}{d t} \cdot N\right)\)
The advantage of this formula over Equation (5) is that it is easier to derive and state. The disadvantage is that it can take a lot of work to evaluate without a computer. Use the new formula to find the torsion of the helix in Exercise 26 .
Equation Transcription:
Text Transcription:
tau
tau=-(dB/ds) . N
dB/ds
dB/ds = dB/dt dt/ds = dB/dt 1/|v|
tau=-1/|v| (dB/dt . N)
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