What does the phrase "in the sense of $\theta$ increasing" mean?

Question

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.

Answer 1

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.