Final answer:
The moment of inertia of an area about the x-axis can be determined by calculating the sum or integral of each 'piece of mass' that makes up the area, multiplied by the square of the distance of each piece of mass to the x-axis.
Step-by-step explanation:
The moment of inertia of an area about the x-axis can be determined by calculating the sum or integral of each 'piece of mass' that makes up the area, multiplied by the square of the distance of each piece of mass to the x-axis.
For example, in the case of a thin rod rotated about an axis through its center (as shown in Figure 10.25), the moment of inertia is given by the formula I = MR².
To justify this sum, you can use the parallel axis theorem, which states that the moment of inertia about an axis parallel to and a distance 'd' away from the original axis of rotation is equal to the moment of inertia about the original axis plus the product of the mass and the square of the distance 'd'.