\"The buttered toast phenomenon is the tendency of buttered toast, when it falls, to land buttered-side down in the majority of instances.\" (Wikipedia) Scientific studies have shown that the effect has little to do with the added weight or the aerodynamics of butter, but rather the table height. Consider the following simplified model: You have a 12.0 cm x 12.0 cm piece of toast of uniform density and of mass m (we will treat the toast has having 0 thickness to greatly reduce the complexity in the geometry). You knock the toast such that it is hanging 9.0 cm beyond the edge (see below, left) of a 75 cm high table, so it is about to tip and fall. We will assume that the toast is initially at rest, not sliding horizontally. The toast rotates without slipping around the table corner until it reaches 7 with the horizontal (see below, middle). After which the toast is rotating so fast that it stops touching the table corner (see below, right). a. What is the initial angular acceleration of the toast, when the toast is still horizontal, while overhanging on the table, and just starting to rotate? b. What is the angular speed of the toast as it stops touching the table? (Since the angle of the toast remains small, we can assume that the angular acceleration remains constant until the toast stops touching the table.) c. What is the downwards linear velocity of center of mass of the toast as it stops touching the table? d. Draw a free body diagram of the toast as it drops through the air. What is the net center- of-mass acceleration of the toast? What is the net angular acceleration of the toast about its center of mass? Ignore air resistance. e. What is the total angular displacement would the toast have rotated through from when it was on the table to when its center of mass is 6 cm off the ground? Remember to account for the initial 7 and include the initial downward center-of-mass speed. We use 6 cm off the ground because it is minimum amount of space the toast needs to turn around. f. If the toast originally sits buttered-side up, does the toast land buttered-side up or down? Bonus: What range of table height would the toast land buttered-side down? Based on your ranges, comment on why the toast lands with buttered-side down in the majority of cases