Why is angular acceleration positive even though it is going clockwise?

[flyingpig]

Homework Statement

Go to http://apcentral.collegeboard.com/apc/public/repository/ap08_physics_c_mech_frq.pdf

Question two

The horizontal uniform rod shown above has length 0.60 m and mass 2.0 kg. The left end of the rod is attached to a vertical support by a frictionless hinge that allows the rod to swing up or down. The right end of the rod is supported by a cord that makes an angle of 30⁰ with the rod. A spring scale of negligible mass measures the tension in the cord. A 0.50 kg block is also attached to the right end of the rod.

The solution is http://www.collegeboard.com/prod_downloads/ap/students/physics/ap08_physics_c_mech_sgs_rev.pdf

The Attempt at a Solution

My question is part d) in the solution key, I just want to ask why is angular acceleration positive? Why did they suddenly change the sum of all torques to positive? It is still going down - clockwise - so why is it positive?

 

[rock.freak667]

They just switched their convention since there would only be clockwise motion. You could have taken counter-clockwise as positive which would give alpha as negative.

At the end, you would get the direction of rotation being clockwise.

 

[flyingpig]

They just switched their convention since there would only be clockwise motion. You could have taken counter-clockwise as positive which would give alpha as negative.

At the end, you would get the direction of rotation being clockwise.

But I thought the convention is that counterclockwise is always positive and clockwise is always negative. I don't understand why they suddenly just changed it for "convenience". I thought the whole counter and clockwise thing is universal to humans

 

[rock.freak667]

But I thought the convention is that counterclockwise is always positive and clockwise is always negative.

Well what I was saying is the even if you used this in the calculation you would just get
α = -21 rad/s² meaning that it is rotating clockwise at 21 rad/s²

I don't understand why they suddenly just changed it for "convenience". I thought the whole counter and clockwise thing is universal to humans

Most times, when you just have motion in one direction only, it is simpler to take that direction as positive.

 

[flyingpig]

But they didn't even say that, they had the torque in part a) consistent with the whole + or - sign convention

 

[rock.freak667]

But they didn't even say that, they had the torque in part a) consistent with the whole + or - sign convention

For that part, the forces would give torques in either clockwise or an anti-clockwise direction. In this case, you would need to set one as positive and the other as negative.

But for the last part, if you cut the cord and take moments about where H is, then you only have clockwise motion.

 

[Phrak]

The designations clockwise and counter-clockwise depend upon which side you view the apparatus. The sign of the angular acceleration does not depend on who is looking at it.

The proper convention for angular acceleration would be inherited from omega = r cross v or tau = r cross F.