Question

Consider the following cases and calculate the moment of inertia and effective acceleration. In each case the can has a diameter of 3 inches.

A. An empty can with a mass of 60g. THis can be considered a thin hoop

B. A can with a mass of 460g containing a thin liquid that does not rotate with the can

C. A can with a mass of 460g containing a gooey substance that rotates with the can without dissipating energy

Answer 1

A) For an empty thin CAN total mas is at the rim

MI = mr²

radius r = 3*0.0254/2 = 0.0381 m

mass m = 60 g = 0.06 kg

MI = 0.06 * 0.0381² = 8.71e-5 kg-m²

B) Mass of the liquid = 460 -60 = 400 g = 0.4 kg

aas the liquid does not rotate , it does not flow to the rim and is like a solid cylinder of radius r = 0.381 m

MI of the liquid cylinder = mr²/2 = 0.4 *0.0381²/2 = 2.90e-4 kg-m²

Total MI ( CAN + liquid) = 2.90e-4 + 8.71 e-5

                                       = 3.771 e-4 kg-m²

C) MI does not change with rotation or speed, It is just the distribution of mass about axis of rotation

            = 3.771 e-4 kg-m² , same as the case of B