Consider the following cases and calculate the moment of inertia and effective a

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 60 g. This can be considered a thin hoop B.A can with a mass of 460 g containing a thin liquid that does not rotate with the can C.A can with a mass of 460 g containing a gooey substance that rotates with the can without dissipating energy. D.A can with a mushy substance that rotates with the can but has a dissipation force of .03 N

Explanation / Answer

Case A. A can or thin hoop an be considered as hollow cylinder whose moment of inertia is well-known to be

I = mR² = mD²/4

Case B. A can with a liquid that does not rotate with the can. It means liquid is stationary and it won't contribute to the rotational motion and hence to the moment of inertia. This case reduces just like case A of thin hoop but with a heavy mass.

I = MR² = MD²/4

Case C. A can with gooey substance rotating with can can be considered as a solid cylinder whose I is given by

I = (1/2)mR² = mD²/8

Case D. There is a frictional force between the can and the mushy substance which will act in the opposite direction of the motion. Hence the moment of inertia will be reduced by the same amount.

I = mR² - (0.03/g)R²

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