WTC1 - A bit of simple geometry
This is just something fairly obvious that occurred to me concerning that well-known conspiracist question: "Why didn't the tops of the WTC towers fall off?" Let's just look at WTC1 for a moment.
Tower height = 1368 feet
1368/110 = 12.4 feet per storey
Collapse initiated at the 97th floor, so the upper block had 13 floors.
13x12.4 = 161 feet high.
Assume the centre of gravity is half this height, so it's about 80 feet above the base of the falling part of the tower. For the top part to fall off, we need it to tip over far enough that this centre of gravity is outside the footprint of the tower.
Now the sides of the WTC towers were 208 feet long, so the edge was 104 feet from the centre. Assuming an axis of rotation right on the centre of the building - the most favourable place for sideways movement of the centre of gravity - if the top part somehow rotated all the way over on to its side, its centre of gravity would therefore still be 24 feet inside the footprint of the tower. Move the axis closer to the edge and the tower can't tip that way, because there would have to be some force lifting it upwards. Place the axis towards the opposite edge and the centre of gravity ends up even further inside the footprint. Therefore, there's no conceivable way the top of WTC1 could have fallen off - it's a simple geometrical impossibility.
WTC2 requires some thought and analysis - it requires about a 42 degree rotation about the most favourable axis to get the centre of gravity outside the footprint, which requires that the lower corner has crushed its way through about 140 feet more of building than the upper corner - but for WTC1 it's fairly trivial to prove that it's a stupid question.