A uniform solid sphere has a moment of inertia I about an axis tangent to its...
Homework Answers
The concepts used to solve this problem are moment of inertia of the body about the center of mass of a solid sphere and parallel-axis theorem.
Use the parallel-axis theorem to find the moment of inertia of the body about the support.
Use the moment of inertia of the body about the support and the moment of inertia of the body about the center of mass to find the moment of inertia of the sphere about an axis through its center in terms of 
.
The expression for the parallel-axis theorem is as follows:
Here, 
is the moment of inertia of the body about the support, 
is the mass of the body, 
is the distance of the center of the body from the support, and 
is the moment of inertia of the body about the center of mass.
The expression for the moment of inertia of the body about the center of mass of a solid sphere is as follows:
Here, the radius of the sphere is 
.
The expression for the parallel-axis theorem is as follows:
Substitute 
for and for 
.
The expression for the moment of inertia of the body about the center of mass of a solid sphere is as follows:
For the sphere:
From the above diagram:
Substitute for and 
for 
.
The moment of inertia of the sphere about an axis through its center is 
.
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A uniform solid sphere has a moment of inertia I about an axis tangent to its...
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Calculate the moment of inertia of the following figure about the axis O. A is a...
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Results given on page 300 TABLE 12.2 Moments of inertia of objects with uniform density Object...
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Calculate the moment of inertia of the following figure about
the axis O. A is a uniform solid cylinder with mass M and radius R.
B is a uniform thin rod with mass M and length 3R. A and B objects
are attached together and rotate together about axis O. The
distance X is and Y is in the figure. The
light blue line is going through the center of the cylinder and the
point “CM” represents the center of mass of...
What is the moment of inertia of the object about an axis at the
center of mass of the object? (Note: the center of mass can be
calculated to be located at a point halfway between the center of
the sphere and the left edge of the sphere.)
Results given on page 300 TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Object and axis Picture Thin rod, about center MCylinder or disk, MR 2 about center Thin rod about end ML Cylindrical hoop, MR2 about center Plane or slab, about center Маг | Solid sphere, about RMR2 diameter Plane or slab, about edge 1Ma2 I spherical shell, about diameter MR2 5. Again, use the table of integration results on page 300 of...
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