hapiworm's Door Slamming

Hi 'hapiworm'--I wasn't kidding when I said I was going to figure this out! I get bored easily. Unfortunately, you've left 'com' by this point, so hopefully you come back because otherwise it will be sad that I took the time to do this. Somehow, this is far more interesting than going down to the pub.

• α = angular acceleration
• L = width of door
• h = height of door
• P = Pressure (both sides 1 and 2 respectively)
• I = Moment of Inertia

This probably doesn't mean a bunch... I got this from a free body diagram of a 'door' (or big flat plate). So let's make an assumption that Hapiworm has a door of uniform density 'ρ' and is a perfect rectangular plate of thickness 't'.

This can be hard to visualize, so I have gone ahead and included an image of the door as we are integrating its 'slices'.

But this isn't terribly helpful since it spins about its axis. Oh yeah--Parellel Axis Theorem. I_hinge = I_CG + MR²

Still a bit strange looking... let's express this in terms of the total mass, M.

So now we can find the new angular acceleration. Woohoo!

Now hopefully hapiworm can sleep easy. It's all so clear! Yay! ;)