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Mass moment of inertia | Area moment of inertia (used in Statics!) | |
---|---|---|
Other names | Second moment of area | |
Description | Determines the torque needed to produce a desired angular rotation about an axis of rotation (resistance to rotation) | Determines the moment needed to produce a desired curvature about an axis(resistance to bending) |
Equations | ||
Units | \( length*mass^2 \) | \( length^4 \) |
Typical Equations | ||
Courses | TAM 212 | TAM 210, TAM 251 |
The parallel axis theorem is used to calculate the moment of inertia for an object around axes other than through the centroid. The parallel axis theorum states:
where \( I_{x'} \) and \( I_{y'} \) are the moments of inertia about the centroid, A is the total area of the shape, and d is the perpendicular distance from the centroid in either the x or y directions.
Moments of inertia of simple shapes can be combined to calculate the moments of inertia of more complex shapes using the parallel axis theorum.
Example problem: what is the \(I_x\) of the composite shape?