Kiertotiheys

Kiertotiheys, often translated as rotational inertia or moment of inertia, is a fundamental concept in physics that quantifies an object's resistance to changes in its rotational motion. Just as mass measures an object's resistance to linear acceleration, kiertotiheys measures its resistance to angular acceleration. It depends not only on the object's mass but also on how that mass is distributed relative to the axis of rotation. Objects with mass concentrated farther from the axis have a greater kiertotiheys.

Mathematically, kiertotiheys (denoted by the symbol I) for a collection of point masses is the sum of the product of each mass and the square of its distance from the axis of rotation. For a continuous object, it is calculated by integrating this product over the entire volume of the object. Different shapes and mass distributions result in distinct formulas for kiertotiheys. For example, a thin rod rotated about its center has a different kiertotiheys than the same rod rotated about one of its ends.

Kiertotiheys is a crucial factor in understanding rotational dynamics. It appears in Newton's second law for rotation, which states that the net torque acting on an object is equal to its kiertotiheys multiplied by its angular acceleration (torque = I * alpha). This means that for a given torque, an object with a larger kiertotiheys will experience a smaller angular acceleration, and vice versa. This principle is evident in various phenomena, from the spinning of a figure skater pulling in their arms to decrease their kiertotiheys and spin faster, to the design of flywheels used to store rotational kinetic energy.