Question

Starting from the basic definition of moment of inertia (eq 9.15), evaluate by integration the rotational inertia of a 50-lb hollow cylinder flywheel about the cylinder axis, whose outer diameter is 16-in and inner diameter is 15-in?

Answer 1

Consider an elemental mass at a distance of from the center of cylinder (shaded ) as shown in the above figure. Thickness of the considered mass element is

Elemental mass is

...... (1)

Rotational moment of inertia of given cylinder about z - axis is

From (1)

...... (2)

Integrate (2) with limits from to . (here are inner and outer radii of cylinder)

Rearrange terms.

...... (4)

Total mass of cylinder is

...... (5)

From (4) and (5),

Thus, the rotational moment of inertia of cylinder about z - axis is

...... (6)

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Given weight of cylinder is

Thus, mass of cylinder is

Here is acceleration due to gravity and its value is

Substitute , and in equation (6)