Question
In: Physics
Starting from the basic definition of moment of inertia (eq 9.15), evaluate by integration the rotational...
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?
Solutions
Expert Solution
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)
--------------------------------------------------------------------
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)
genius_generous answered 2 years agoRelated Solutions
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