Mass Moment of Inertia:

The product of the mass and the square of the distance of the center of gravity of the mass from an axis is known as the mass moment of inertia. It is a physical property of an object that measures its resistance to rotational motion around a particular axis. The mass moment of inertia is denoted by the symbol "I" and is given by the equation:

I = m * r^2

where:
- I is the mass moment of inertia
- m is the mass of the object
- r is the distance between the center of gravity of the mass and the axis of rotation

Explanation:

The mass moment of inertia is a measure of how the mass of an object is distributed around a given axis of rotation. It takes into account both the mass of the object and its distribution with respect to the axis. The farther the mass is from the axis, the greater the mass moment of inertia.

The concept of mass moment of inertia is important in various engineering applications, particularly in the design and analysis of rotating machinery, such as engines, turbines, and flywheels. It helps determine how the object will respond to rotational forces and torques.

The mass moment of inertia depends on the shape and mass distribution of the object. For simple shapes, such as cylinders or spheres, there are formulas that can be used to calculate the mass moment of inertia. For more complex shapes, numerical methods or computer simulations may be required.

The mass moment of inertia has several important properties:
1. It is always positive or zero, as it is a measure of the object's resistance to rotation.
2. The mass moment of inertia of a point mass is zero, as the mass is concentrated at a single point and has no distribution.
3. The mass moment of inertia is additive. For a system of particles, the total mass moment of inertia is the sum of the individual mass moments of inertia.

In conclusion, the product of the mass and the square of the distance of the center of gravity of the mass from an axis is known as the mass moment of inertia. It is a fundamental property of an object that characterizes its rotational behavior.