What is the correct representation of torque in the provided physics problem?

[tmiddlet]

Hello pf!
I'm self-studying physics on MIT OCW, and I'm confused about one of the challenge problems. (attached)
I'm looking at problem #2, and I thought I had it understood, but when I looked at the solution the first thing that is stated is that τ = Rf - bF (f = the force of friction). For some reason, I got τ = bF - Rf. I took the cross product of <0,-b> and <F,0> which if bF and the cross product of <0,-R> and <-f,0>, which is -Rf.
I just don't see how we came with the opposite of the answer. Where did I go wrong?

 

[ehild]

You are right about the sign of the torque, but the yo-yo will accelerate to the right so the angular acceleration of rolling is negative. The solution considered the torque positive if it resulted in linear acceleration in the direction of the applied force.

ehild

 

[rcgldr]

To clarify, you didn't do anything wrong. Both angular acceleration and Rf torque are negative, while bF torque is positive. Even though the linear acceleration corresponds to negative angular acceleration, the provided solution should not have changed the sense of the normal sign convention for torque and angular acceleration.