AP Question Torque Sign Conventions

[jzhang]

On the 2012 AP Physics C Mechanics test, I got confused by the sign conventions for torques on question 3. (http://apcentral.collegeboard.com/apc/public/repository/2012_frq_physics_cm.pdf)

In the scoring guidelines, (http://apcentral.collegeboard.com/a...12_physics_c_mechanics_scoring_guidelines.pdf), friction was negative so this would be standard reference. Later, the scoring rubric had torque produced by friction positive. However, in standard reference, the torque from friction would be clockwise or negative. Does it matter or is there something I'm missing?

 

[Simon Bridge]

Welcome to PF;
Torque is a pseudovector in 3D and follows the direction conventions for a right-handed coordinate system.
In 2D, an anticlockwise torque points out of the page, and would be positive by this convention.

However, when summing torques in 2D you are free to pick whichever direction you like for positive, just like you can with regular vectors. So long as you are consistent, it will all work out.

The AP exam question:
When you start a question like that, you should specify the directions you use for positive.
Note: The question asks only for the equation to find the magnitude - magnitudes are always positive.

Do the question with either convention and see if it makes a difference. I suspect you'll find the minus signs cancel out in this example.

General rule: pick your sign conventions to make the maths easy.
i.e. If all the translation is downwards, then pick downwards to be positive.
If all the rotation is clockwise, then pick clockwise to be positive.
That way you have fewer minus signs to work out.