The moment of inertia around the center of mass is a measure of an object's resistance to rotational motion. It is calculated by summing the products of each point mass in the object and its distance from the center of mass squared.
To calculate the moment of inertia using the summation formula, you need to first identify all the point masses in the object and their distances from the center of mass. Then, square each distance and multiply it by the mass of the point mass. Finally, add all of these products together to get the total moment of inertia.
No, the moment of inertia cannot be negative. It is always a positive value since it represents the object's resistance to rotation.
Finding the moment of inertia around the center of mass is important because it simplifies the calculation and makes it easier to analyze the object's rotational motion. Additionally, the moment of inertia around the center of mass is the minimum value for the object's moment of inertia, meaning it requires the least amount of energy to rotate around this point.
The distribution of mass in an object affects the moment of inertia by changing how the mass is distributed around the axis of rotation. Objects with most of their mass concentrated closer to the axis of rotation will have a smaller moment of inertia, while objects with more mass distributed farther from the axis of rotation will have a larger moment of inertia.