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Indeed, without superposition, one can't add vectors [and tensors].
(The moment of inertia is really a tensor.)
(The moment of inertia is really a tensor.)
The moment of inertia is a measure of an object's resistance to changes in rotational motion. It is the sum of the products of the mass of each particle in the object and the square of its distance from the axis of rotation.
For a simple object with a known mass distribution, the moment of inertia can be calculated using the formula I = mr², where m is the mass of the object and r is the distance from the axis of rotation to the particle.
When two or more objects are combined, the total moment of inertia is the sum of the individual moments of inertia. This is similar to how masses are added together in linear motion.
Adding moments of inertia allows us to calculate the combined rotational motion of multiple objects. This is important in many real-world applications, such as designing machines or analyzing the motion of celestial bodies.
The moment of inertia of an object can be affected by its mass distribution, shape, and axis of rotation. For example, objects with more mass concentrated further from the axis of rotation will have a higher moment of inertia. Additionally, changing the axis of rotation can also change the moment of inertia of an object.