A thin hoop of mass

**M**, radius

**R**, and rotational inertia

**MR**^{2}is released from rest from the top of the ramp of length

**L** above. The ramp makes an angle

with respect to a horizontal tabletop to which the ramp is fixed. The table is a height

**H** above the floor. Assume that the hoop rolls without slipping down the ramp and across the table. Express all algebraic answers in terms of given quantities and fundamental constants.