Question on AP Physics C FRQ 2013. #3

[RoboNerd]

Homework Statement

http://media.collegeboard.com/digitalServices/pdf/ap/apcentral/ap13_frq_physics_c_mechanics.pdf

The problem is above. It is number 3.

The solutions are below:
http://media.collegeboard.com/digit...entral/ap13_physics_cm_scoring_guidelines.pdf

Homework Equations

Torque= I * angular acceleration, F=ma

The Attempt at a Solution

My questions are the following:

Why do they in part a of the solution do the expression 2Fa-mg=0?
I understand that they have Fa acting on the object and mg, but why do they have the left rope's tension equal Fa?And then in part B, why do they have the expression Fa + T - Mg = Ma, meaning why do they have Fa != T. And then they substitute the T from the torque equation. Why is doing the problem in this manner necessary, with a separate value for T, which does not equal Fa?

 

[Doc Al]

Why do they in part a of the solution do the expression 2Fa-mg=0?
I understand that they have Fa acting on the object and mg, but why do they have the left rope's tension equal Fa?

You are told that the disk is at rest (in equilibrium).

In part B the disk is no longer in equilibrium.

 

[RoboNerd]

Yeah, but when it is at equilibrium, then couldn't I just write it as Fa-mg = 0.

Maybe it is because the Fa is causing a torque on the right side and we need an equal force to counteract it from the left side to have sum of torques cancel?

 

[Doc Al]

Yeah, but when it is at equilibrium, then couldn't I just write it as Fa-mg = 0.

That assumes the tension on the left segment is zero. And it wouldn't satisfy rotational equilibrium.

Maybe it is because the Fa is causing a torque on the right side and we need an equal force to counteract it from the left side to have sum of torques cancel?

Right!

 

[RoboNerd]

Yeah that makes sense. Thanks a lot!