Question makes no sense, but should be simple

[SoulInNeed]

1. There is a circular disk with a string wrapped around its center. We attached a mass to the string, and the force caused it to rotate. Now, the hypothetical question is "The hanging mass m is exerting a constant downward force of magnitude mg on our system. What would happen to the angular acceleration of our system if the hanging mass were removed and replaced by a constant downward force of equal magnitude, but with no associated mass?"

Homework Equations

Net Torque=Ia
I=mr^2
sum of force=mg-T=ma

The Attempt at a Solution

My first instinct was to say that nothing would change because the force would stay the same, but now I think that the angular acceleration would increase, because the lack of any associated mass would cause the inertia to decrease. Any help guys?

 

[rock.freak667]

I'd say your first instinct is right.

Homework Equations

sum of force=mg-T=ma

Remember, it is the sum of forces being considered. You don't consider the mass 'm' alone, you consider the weight 'mg'. So essentially, you are replacing the weight (a force) with a similar downward force with the same magnitude.

 

[SoulInNeed]

I'd say your first instinct is right.



Remember, it is the sum of forces being considered. You don't consider the mass 'm' alone, you consider the weight 'mg'. So essentially, you are replacing the weight (a force) with a similar downward force with the same magnitude.

That's what I was thinking, but that equation applies to translational acceleration, and this equation deals with angular acceleration. For that, we use the equation torque=Inertia*angular acceleration, right? Wouldn't the loss of a mass (even if its force remains) simply reduce inertia, and thus, increase angular acceleration?

 

[rock.freak667]

That's what I was thinking, but that equation applies to translational acceleration, and this equation deals with angular acceleration. For that, we use the equation torque=Inertia*angular acceleration, right? Wouldn't the loss of a mass (even if its force remains) simply reduce inertia, and thus, increase angular acceleration?

Wouldn't it work out the same way if you take moments about the disk?

mgr-Tr= Iα
with I being the mass moment of inertia of the disk.

 

[SoulInNeed]

Wouldn't it work out the same way if you take moments about the disk?

mgr-Tr= Iα
with I being the mass moment of inertia of the disk.

Are you saying it would just even out on both sides of the equation?

 

[Phrak]

Perhaps there is another way to consider the problem without the details of the disk. In one case energy goes into rotating the disk plus the kinetic energy of the mass. In the second case only the disk gains kinetic energy.