If we push a regular object from a table ( take a cuboid ) , can you predict that whether it will turn while falling or not and what face of it will hit the ground . Like if you accidentally push a book from a table and it falls down , why sometimes it falls on its face down and not face up. Can you predict this ?
In order to predict which side an object will land on, generally we need a few pieces of information:
The shape of the object and its size. This determines how many "sides" the object has in the first place (where "sides" is defined here to be "configurations that an object can land in, up to a rotation about the vertical axis and an arbitrary translation"). For some objects, the "sides" are simple to define: a cube has six, a tetrahedron has four, and an octahedron has eight, for example. For others, they may not look like "sides" in the normal sense: a sphere has one "side" by our definition, because there is one configuration that it can land in, and a cylinder, even a thin one like a coin, has three sides, since it can technically land on the round edge. The shape and size of the object also determine the effect of air resistance, which is a very significant factor in objects with large cross-sectional area and low mass (like a feather).
The weight distribution in the object. This determines its center of gravity, which in turn determines the "tipping points" for each side and influences how the object ultimately reacts when it hits the ground. For example, a pair of "loaded dice" gives you different results than a pair of regular dice, because the loaded dice have an uneven weight distribution that makes the tipping-point angle quite large for one of the sides. That side is likely to be on the bottom when the die lands.
The initial conditions when the object was pushed from the table. There are a few relevant quantities here: initial height of the object above the ground (i.e. the height of the the table), the initial horizontal and vertical velocities of the object, the initial angular velocity of the object and the axis of rotation, and the initial orientation of the object as it leaves the table. The initial conditions, along with the object's shape, size, and weight distribution, determine the object's final orientation when it first hits the ground.
How the object reacts when it hits the ground, and how the ground reacts when it is hit by the object. This includes all of the information relating to the elasticity (i.e. does it bounce?) and/or fracture toughness (i.e. does it shatter or break?) of both the object and the ground. This information matters from the first impact with the ground to the final orientation.
Once we have all of that information, we can use a simulation engine that takes all of these into account to predict with reasonable accuracy how an object will land.