Category:Definitions/Moment of Inertia
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This category contains definitions related to Moment of Inertia.
Related results can be found in Category:Moment of Inertia.
Let $B$ be a rigid body which is rotating in space about some axis $\LL$.
The moment of inertia of $B$ about $\LL$ is defined as follows:
Discrete
Let $B$ be composed of a countable number of particles $P_1, P_2, \ldots$ such that:
- each $P_i$ has mass $m_i$
- each $P_i$ has perpendicular distance $r_i$ from $\LL$.
The moment of inertia of $B$ about $\LL$ is given by:
- $I := \ds \sum m_i {r_i}^2$
Continuous
Let each point in $B$ have:
- a position vector $\mathbf r$ with respect to a given frame of reference.
- a density $\map \rho {\mathbf r}$
- a perpendicular distance $\map p {\mathbf r}$ from $\LL$
The moment of inertia of $B$ about $\LL$ is given by:
- $I := \ds \int_B \paren {\map p {\mathbf r} }^2 \map \rho {\mathbf r} \rd v$
where $\d v$ is an infinitesimal volume element of $B$.
Pages in category "Definitions/Moment of Inertia"
The following 6 pages are in this category, out of 6 total.