If a solid semicylindrical block (a block-letter D) is placed on its curved side on a horizontal table, the top (the flat side) will be parallel to the table.

The table is tilted by an angle, a, perpendicular to the axis of the cylinder. What angle will the top of the block form with the table now?

Assume angle a is small enough to prevent the block from slipping or tipping over.

When the Big D is lying on the horizontal table, the centre of gravity (cog) of the Big D  is lying in the plane that goes through the axis of the cylinder and that is perpendicular to the flat side of the Big D.
Once the table is tilted, the cog must lay above the contact point between Big D and the table.  This implies that the cog is of importance to define the angle, which on its turn implies that the dimension of the flat side is of importance: How Big D is the Big D?  Is it half a cylinder or more like a cylinder with just a small slice off?

As the title said, not really helpfull first thoughts.

A very nice problem Jer, I like it a lot.

Posted by Hugo on 2006-01-16 15:57:02