The moment of inertia is defined as the total of the masses of all the particles in the body multiplied by the square of their respective perpendicular distances from the axis of rotation.

The area of the cross-section on each side of the plastic neutral axis is multiple by the distance between the local centroids of the two areas is called the plastic section modulus.

## Key Takeaways

- Plastic modulus measures a material’s ability to withstand plastic deformation before failure.
- Moment of inertia evaluates an object’s resistance to rotational motion based on its mass and shape.
- Both properties are crucial for understanding structural behavior and designing robust engineering systems.

**Plastic Modulus vs Moment of Inertia**

The plastic modulus is a measure of a structural member’s ability to resist bending after it has reached its yield strength and has undergone plastic deformation. The moment of inertia is a measure of how far the material in a member is from the neutral axis that has no deformation during bending.

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Plastic modulus is a cross-sectional property, not a material property, but a moment of inertia is not a property because it refers to the force required to change speeds.

The plastic section modulus is based on the assumption that the entire segment gives.

Moment of inertia is a physics concept that describes the motion of a system of particles and a rigid body, whereas plastic modulus is a structural engineering concept.

Both, the plastic modulus and the moment of inertia require the presence of an object or a material. Plastic modulus is concerned with the point of deformation, whereas moment of inertia is concerned with the speed of a given item.

**Comparison Table **

Parameters of Comparison | Plastic Modulus | Moment of inertia |
---|---|---|

Notation | Given by ‘Z’ | Given by ‘I’ |

Formula | Zp = ACyC + ATyT | I = m × r^2 |

SI unit | mm^3 | Kg m^2 |

Classification | It is a type of section modulus | It is classified into a low high moment of inertia. |

Uses to calculate | The plastic moment or full capacity of a cross-section | rotational kinetic energy and angular momentum |

Dependence | the location of the plastic neutral axis | shape and size of the body, position & orientation of the axis of rotation |

## **What is Plastic Modulus? **

First, let us know about the term section modulus, it’s a geometrical term for a given cross-sectional that helps to plan flexural members or beams.

The elastic and plastic section modulus are the two variants of section modulus. The placing of the plastic neutral axis act on the plastic modulus.

The PNA is a block that splits the cross-section so that the tension force produced by the braced area matches the compressive forces produced by the compressed location.

Therefore, the area surrounding above the surface and below the PNA will be the same for loacations with steady yielding stress, but this is not generally the concern for compound sections.

It’s employed for materials that have been approved for elastic yielding and where plastic behavior is assumed to be a long-term limit.

To cut down irreversible deformations, a maximum plan follows to stay below the plastic limit, repeatedly differentiating the plastic capacity to boost forces or stresses.

The plastic modulus is helping to determine a cross-plastic section’s moment (Mp) or full capacity Mp = FyZ. It is the relationship among the two terms, which is determined by the yield strength of the material (Fy) by Mp = Fy.

Plastic modulus and elastic modulus are correlated by a form factor, represented by k, which is used to show capacity above the material’s elastic limit.

**What is a Moment of inertia? **

The property of inertia is a body’s resistance to change in its state of rest or motion.

Thus, the moment of inertia is known as the quantity given by a body opposing angular acceleration, which is the total mass of every particle multiplied by the square of its distance from the rotation axis.

The moment of inertia is a scalar quantity. The moment of inertia is determined by the axis of rotation’s position and direction, the body’s shape and size, and the distribution of the body’s mass around the axis of revolution.

The inertia moment (I) is also the ratio of a system’s net angular momentum (L) to its angular velocity (ω) around a principal axis, i.e. I = L/ω

In simple words, it’s a capacity that determines the amount of torque needed for a definite angular acceleration in a rotational axis.

The angular mass or rotational inertia is another name for the moment of inertia. The SI unit of moment of inertia is kgm2. Moment of Inertia can be expressed as: I = Σ miri2.

The moment of inertia is an important topic that appears in almost all physics situations whereas angular momentum is normally calculated using the moment of inertia.

**Main Difference Between Plastic Modulus and Moment of inertia**

- Plastic modulus is given by ‘Z’ and moment of inertia by‘I’ respectively.
- The formula of Plastic modulus is Zp = ACyC + ATyT and moment of inertia I = m × r^2.
- SI unit of plastic modulus and moment of inertia is mm^3 and kgm^2 respectively.
- Plastic and elastic section modulus are types of section modulus, whereas low and high moment of inertia is two types of a moment of inertia.
- The plastic moment of a cross-section is determined through the plastic modulus, on the other hand, a moment of inertia is used to calculate rotational kinetic energy and angular momentum.
- The location of the PNA determines the plastic modulus, and the moment of inertia is determined by the shape and size of the body, as well as the position and orientation of the rotational axis.

**References**

Piyush Yadav has spent the past 25 years working as a physicist in the local community. He is a physicist passionate about making science more accessible to our readers. He holds a BSc in Natural Sciences and Post Graduate Diploma in Environmental Science. You can read more about him on his bio page.