Explanation: two toilet paper rolls are dropped such that they land on the floor at the same time. One roll of toilet paper is unravelling as it falls from the height of the desk (while one person holds the toilet paper to the desk as the roll falls and continues to unravel), and the other roll is falling from an unknown height, that is of course higher than the unravelling roll, so that both rolls land on the floor at the same time. The attached picture contains all the information on the objects, visualizing the scenario.
Roll 1 is falling from the table and unravelling as it falls (it has a mass of 0.10129kg)
Roll 2 is falling from the unknown height to meet roll 1 on the ground at the same time (this has a mass of 0.09884kg)
The height of the desk from which roll 1 is falling from is 0.915m.
The measured diameter of the rolls across the entire thing = 10.5cm (0.105m), which gives a radius of 5.25cm (0.0525m).
The measured diameter of the rolls across the hollow cardboard center = 5.5cm (0.055m), which gives a radius of 2.25cm (0.0225m).
The measurements were equal on each roll.
These rolls are treated as hollow thick-walled cylindrical objects, such that their moment of inertia `I ` is given by the equation
`I = 1/2 M (r^2 + R^2) ` where M is the mass, r is the inner radius and R is the outer radius
Calculate the height from which roll 2 must fall in order that it reach the floor at the same time as roll 1.
NB The change in total radius of the unravelling roll, roll 1, from desk to floor is assumed to be negligible compared to its original length R, so that the moment of inertia for the roll, and indeed the roll's mass, is approximately constant throughout its fall.