How does a rod rotate due to gravity?

[HoodedFreak]

Homework Statement

Imagine a uniform, symmetric rod, free to rotate around an axis going into the computer screen through the center of the rod. Now say that we start off the rod so that it is not horizontal or vertical, but somewhere in between. My intuition tells me that the rod will start to fall and rotate, but why does this happen? Isn't it true that by symmetry, if there is torque exerted by a particle of the rod on one side due to the force of gravity, an equal and opposite torque would be exerted by the particle the same distance on the other side of the rod, so the rod should stay stationary. But I know this isn't the case, so where am I going wrong here?

Homework Equations

T = r*l

where r is distance and l is the lever arm

The Attempt at a Solution

I've attached a diagram of the situation as I see it.

 

[Doc Al]

My intuition tells me that the rod will start to fall and rotate

Perhaps your intuition is wrong.

 

[HoodedFreak]

Perhaps your intuition is wrong.

Is my intuition wrong? I mean, for example if I take my pencil and hold it between my fingers as close as I can to the middle the higher end starts to rotate downwards, maybe that's because the pencil is slightly unbalanced or I am not not holding the pencil exactly in the middle.

 

[Bystander]

Conservation laws?

 

[Doc Al]

Is my intuition wrong?

I'd say it was. I agree with your reasoning in your first post; the torques from each side will cancel.

I mean, for example if I take my pencil and hold it between my fingers as close as I can to the middle the higher end starts to rotate downwards, maybe that's because the pencil is slightly unbalanced or I am not not holding the pencil exactly in the middle.

You'll have to arrange a more careful test.

 

[HoodedFreak]

I'd say it was. I agree with your reasoning in your first post; the torques from each side will cancel.You'll have to arrange a more careful test.

Well mystery solved, that makes a lot more sense. Thanks

 

[CWatters]

Is my intuition wrong? I mean, for example if I take my pencil and hold it between my fingers as close as I can to the middle the higher end starts to rotate downwards, maybe that's because the pencil is slightly unbalanced or I am not not holding the pencil exactly in the middle.

That's the obvious answer. If you are balancing the pencil on one finger be aware that fingers are round so the pivot point can move as the pencil rotates around it. I suspect it starts offset to the lower side.