I've encountered this phrase many times while doing problems in dynamics. It appears when I am trying to write a vector equation using scalar quantities and almost always a derivative is involved. I don't have a clear idea on this. Some explanation would be helpful.
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Not Euler
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have you solved your doubt? – user Dec 18 '17 at 13:26
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It means that the equation hold if the sign convention on $\theta$ and $L$ is the same, otherwise you would have a minus sign in the equation.
It is similar to Newton's law: $$F=ma$$ where we are assuming that acceleration is positive for a positive applied force.
user
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I had figured out the need for writing something like that I.e. to make sure both sides have the same sign. But I still don't understand how that line serves the purpose. If a positive $L$ increases $\theta$ that just means that the time-derivative of $\theta$ is positive for a positive $L$. It doesn't say anything about the second derivative. – Not Euler Dec 16 '17 at 16:02
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You have to look as the equation is obtained, of course you will find the same convenction for the sign of $\theta$ and $L$. The law we are talking abuot states that the anguar acceleration is positive if L is positive, that's true also if the angualr velocity is negative. – user Dec 16 '17 at 16:07
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Angular acceleration is positive if $L$ is positive - I don't understand how we got this. – Not Euler Dec 16 '17 at 16:09
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It's a matter of convention. Let's consider $F=ma $ which is completely analogous for a one dimensional problem. If you set the positive direction for displacement, velocity and acceleration with the positive x-axis and also the Force in the same direction, Newton's law is F=ma. Otherwise if for F is choosen the reverse direction Newton's law is F=-ma. For the moment L and angle $\theta$ the set is the same. Every law involving vectors and direction depend upon the sign conventions adopted. – user Dec 16 '17 at 16:15