Moment of Inertia, Strong/Weak axis?

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SUMMARY

The discussion centers on the concept of moment of inertia, specifically differentiating between mass moment, area moment, and polar moment of inertia. The mass moment of inertia resists angular acceleration and is measured in kg·m², while the area moment of inertia, which resists bending, is measured in m⁴ and is crucial for stress calculations. The polar moment of inertia also resists torsion and is similarly measured in m⁴. The confusion between polar moment and area moment of inertia is highlighted, particularly in applications involving shafts.

PREREQUISITES
  • Understanding of basic physics concepts such as angular acceleration and linear acceleration.
  • Familiarity with stress calculations in engineering, particularly the formula σ = Mc/I.
  • Knowledge of the geometric properties of shapes, particularly in relation to axes of rotation.
  • Basic understanding of units of measurement in physics, specifically kg·m² and m⁴.
NEXT STEPS
  • Study the derivation and applications of the mass moment of inertia in rotational dynamics.
  • Learn about the calculation and significance of the area moment of inertia in structural engineering.
  • Explore the polar moment of inertia and its role in torsional analysis of shafts.
  • Investigate the relationship between different moments of inertia and their applications in real-world engineering problems.
USEFUL FOR

Engineering students, mechanical engineers, and professionals involved in structural analysis and design will benefit from this discussion, particularly those focusing on the mechanics of materials and rotational dynamics.

subwaybusker
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Hello, can anyone explain to me what the moment of inertia is? we learned the mass moment, second moment and the first, and I'm getting confused as to what they all are. and can anyone explain what the strong/weak axis is? is it resistance to bending or rotation? i just can't visualize where the strong/weak axis would be on a ruler and our prof drew x and y axes but they don't make sense to me unless...you tilt the ruler?

he drew something like with the width of the ruler (not thickness) along the y axis.

y
|
---------------|------------x
|
 
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Yea, they can be quite confusing and when doing a calculationg it's important to check your units to make sure that you're calculating the proper moment of inertia. With that in mind, here are some of them:

Mass Moment of Inertia - Resists angular acceleration. Analogous to mass and linear acceleration:
units: kg \cdot m^2
Used in the Equation T = I\omega

Area Moment of Inertia (second moment) - Resists Bending
units: m^4
Used in the Stress Calculations like \sigma = \frac{Mc}{I}

Polar Moment of Inertia - Resists Torsion
units: m^4
Used in the Equation \tau = \frac{Tr}{J}

In my experience, Polar Moment of Inertia and Area Moment of inertia get confused along the axis of a shaft or other long part; they are not the same thing. It can be shown that the polar moment of inertia is the sum of the other two off axis moments of inertia. If the x-axis runs along a shaft, then J = I_{yy} +I_{zz}}
 
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