Mass properties

The mass properties of an object or system are crucial for understanding and analyzing its dynamic and static properties. These properties include mass, center of gravity (COG), moments of inertia (MOI) and products of inertia (POI). Here are the most important aspects and definitions of these mass properties:

Mass

Mass is a basic measure of the amount of matter in an object. It is measured in kilograms (kg) and is a scalar quantity that describes the inertia of an object to a change in its state of motion. Mass is one of the most fundamental properties of a physical system and directly influences its dynamics and behavior under the influence of forces.

Center of mass

The center of gravity (COG) is the point in an object or system at which the entire mass can be considered to be concentrated. When an external force acts on this point, the object is moved translationally without rotating. The COG is crucial for analyzing the motion and equilibrium of an object. For symmetrical and homogeneous objects, the COG is often at the geometric center.

Moments of inertia

The moments of inertia (MOI) describe the resistance of an object to a change in its rotational movement. They are the rotational equivalent of mass in translational motion and depend on the mass distribution relative to the axis of rotation. MOIs are measured in kilogram-square meters (kg-m²) and are crucial for analyzing the rotational dynamics of an object. Several moments of inertia can be defined for an object, depending on the selected axis of rotation.

Inertia products

The products of inertia (POI) are a measure of the asymmetry in the mass distribution of an object. They describe how the mass distribution of an object correlates with each other around different axes. In contrast to the moments of inertia, which are always positive, the products of inertia can have positive, negative or zero values. The POIs are important for the complete description of the inertial properties of an object, especially when it comes to analyzing the rotation around any axis.

Meaning and application

Mass properties are of central importance in many areas of engineering and physics, including mechanics, aerospace engineering and robotics. They are critical to the planning, design and analysis of systems and objects to ensure they meet desired performance and safety requirements. By understanding and controlling these properties, engineers and scientists can accurately predict and control the dynamics and behavior of objects.