Massakracht van traagheid: Probleemoplossing

The moment of inertia of a wheel's axle is important to understand its behavior when rotating.

The axle can be approximated to a solid cylinder with constant density.

Consider an elemental disc parallel to the circular face of the cylinder at a certain distance from the perpendicular axis.

The mass moment of inertia for the disc about its diameter equals one-fourth the product of the mass and radius squared.

Applying the parallel-axis theorem, the moment of inertia of the disc with respect to the perpendicular axis can be estimated.

The differential mass equals the product of the cylinder's linear mass density and the disc's thickness.

Integrating the expression over the cylinder's length gives its moment of inertia about the perpendicular axis passing through the centroid.

For calculating the moment of inertia about the longitudinal axis, a thin cylindrical shell is considered.

Again, the differential mass is substituted into the moment of inertia equation and integrated over the cylinder's radius.

So, the moment of inertia about both these axes is a geometrical entity.