# MASSPROP (Command)

Calculates the mass properties of selected 2D regions or 3D solids.

Find

### 2D Regions

The following table shows the mass properties that are displayed for all regions.

Mass properties for all regions

Mass property

Description

Area

The surface area enclosed by the region.

Perimeter

The total length of the inside and outside loops of a region.

Bounding box

The coordinates of the two points that define the bounding box. For regions that are coplanar with the XY plane of the current user coordinate system, the bounding box is defined by the diagonally opposite corners of a rectangle that encloses the region. For regions that are not coplanar with the XY plane of the current UCS, the bounding box is defined by the diagonally opposite corners of an enclosing 3D box.

Centroid

The coordinate values of a point located at the geometric center. For regions that are coplanar with the XY plane of the current UCS, this is a 2D point. For regions that are not coplanar with the XY plane of the current UCS, this is a 3D point.

If the regions are coplanar with the XY plane of the current UCS, the additional properties shown in the following table are displayed.

Additional mass properties for coplanar regions

Mass property

Description

Moments of inertia

A value used when computing the distributed loads, such as fluid pressure on a plate, or when calculating the forces inside a bending or twisting beam. The formula for determining area moments of inertia is

area_moments_of_inertia = area_of_interest * radius 2

The area moments of inertia has units of distance to the fourth power.

Products of inertia

Property used to determine the forces causing the motion of an object. It is always calculated with respect to two orthogonal planes. The formula for product of inertia for the YZ plane and XZ plane is

product_of_inertia YZ,XZ = mass * centroid_to_YZ * dist centroid_to_XZ

This XY value is expressed in mass units times the length squared.

Another way of indicating the moments of inertia of a 3D solid. The formula for the radii of gyration is

Radii of gyration are expressed in distance units.

Principal moments and X,Y,Z directions about centroid

Calculations that are derived from the products of inertia and that have the same unit values. The moment of inertia is highest through a certain axis at the centroid of an object. The moment of inertia is lowest through the second axis that is normal to the first axis and that also passes through the centroid. A third value included in the results is somewhere between the high and low values.

### 3D Solids

The following table shows the mass properties that are displayed for 3D solids.

Mass properties for solids

Mass property

Description

Mass

The measure of inertia of a body. The density is always a value of 1.00, so the mass and volume have the same value.

Volume

The amount of 3D space that a solid encloses.

Bounding box

The diagonally opposite corners of a 3D box that encloses the solid.

Centroid

A 3D point that is the center of mass for solids. A solid of uniform density is assumed.

Moments of inertia

The mass moments of inertia, which is used when computing the force required to rotate an object about a given axis, such as a wheel rotating about an axle. The formula for mass moments of inertia when the axis is outside the object is

mass_moments_of_inertia = object_mass * radius axis 2

When an axis of rotation passes through the object, the mass moment of inertia depends on the shape of the object.

Products of inertia

Property used to determine the forces causing the motion of an object. It is always calculated with respect to two orthogonal planes. The formula for product of inertia for the YZ plane and XZ plane is

product_of_inertia YZ,XZ = mass * dist centroid_to_YZ * dist centroid_to_XZ

This XY value is expressed in mass units times the length squared.

Another way of indicating the moments of inertia of a solid. The formula for the radii of gyration is

Radii of gyration are expressed in distance units.

Principal moments and X,Y,Z directions about centroid

Calculations that are derived from the products of inertia and that have the same unit values. The moment of inertia is highest through a certain axis at the centroid of an object. The moment of inertia is lowest through the second axis that is normal to the first axis and that also passes through the centroid. A third value included in the results is somewhere between the high and low values.

The following prompts are displayed.

Select objects

Use an object selection method to select either regions or 3D solids for analysis. If you select multiple regions, only those that are coplanar with the first selected region are accepted.

Write analysis to a file

Specify whether you want to save the mass properties to a text file. By default, the text file uses a .mpr file extension.