Question
The moment of inertia about a diameter of a solid sphere of constant density and radius $a$ is $(2 / 5) m a^{2},$ where $m$ is the mass of the sphere. Find the moment of inertia about a line tangent to the sphere.
Step 1
Step 1: The moment of inertia of a solid sphere about its diameter is given by $I_{cm} = \frac{2}{5}ma^2$ where $m$ is the mass of the sphere and $a$ is the radius. Show more…
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(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be $2 M R^{2} / 5$, where $M$ is the mass of the sphere and $R$ is the radius of the sphere. (b) Given the moment of inertia of a disc of mass $M$ and radius $R$ about any of its diameters to be $M R^{2} / 4$, find its moment of inertia about an axis normal to the disc and passing through a point on its edge.
The moment of inertia of a solid sphere of mass $\mathrm{M}$ and radius $R$ about a tangent to the sphere is (a) $\frac{2}{5} \mathrm{MR}^{2}$ (b) $\frac{6}{5} \mathrm{MR}^{2}$ (c) $\frac{4}{5} \mathrm{MR}^{2}$ (d) $\frac{7}{5} M R^{2}$
Moment of inertia of solid sphere. Show that the moment of inertia about a diameter of a solid sphere is $\frac{2}{5} M r^{2} .$ This can be simply done by considering the sphere to be a stack of circular disks of infinitesimal thickness fitting within a spherical bounding surface.
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