Balancing a pencil

Originally, I meant to prove my (nonexistent) skills at balance by skillfully balancing the pencil on the eraser. However, due to the odd shape of the eraser, the unequal mass distribution and shape of the pencil, and the slight tilt of the surface I was trying to balance it all on, the thing refused to obey and fell over. And fell over again. And again. Finally, I discovered something amazing... It is IMPOSSIBLE TO GET A PENCIL TO BALANCE ON A LUMPY ERASER. I'm sure that this is due to some special property of unstable equilibrium, since it won't stay in equilibrium with even the light force of the air flowing past pushing it, but it just proved how stupid my idea was in the first place. I've surrendered to the fact that I would write a blog post about how it WON'T balance at all I mean, easily.

The support, the eraser, exerts a normal force upward on the pencil equal to the weight of the pencil. The weight of the pencil is a force at the middle of the pencil in theory, if you pretend that its mass is equally distributed, and it is a perfect cylinder, not a weird composite of graphite, wood, rubber, and some sort of metal. Since in my head, pencils are perfect cylinders that are easy to understand using physics concepts, the weight will come from exactly the middle of the pencil. This means there is a torque force on the pencil of magnitude r x f, or the distance from the center of the pencil to the axis of rotation multiplied by the weight. Since the net torque is clearly pushing the pencil clockwise, it doesn't balance, and tilts to the right.

And not that anyone cares, but I've managed to sneak Beren into another blog entry... completely by accident this time. It's not my fault that most of the regular pencils in the house are labeled with his name... (Believe me, mechanical ones are even harder to balance. I tried.)

Happy Early Thanksgiving, Everyone!