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.

The coefficient of friction must be great enough to keep the "D"
from slipping and the center of mass of the "D" must be directly
over the point of contact between the "D" and the table to keep
the "D" from tipping. Using this, I get the angle the top of the
block forms with the table as

            arcsin(sin(a)/h) - a

where h = 4/(3*PI).

The above required a lot of calculations, so take it with a
grain of salt.

Posted by Bractals on 2006-01-16 22:41:51