mass moment of inertia of cylinder and thin disc
h = 0
title: Moment of inertia text: Moment of inertia The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a tensor that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation rate. It is an extensive (additive) property: for a point mass the moment of inertia is just the mass times the square of the perpendicular distance to the rotation title: Moment of inertia text: inertia matrix and the scalar moment of inertia formula_333 around an axis in the direction formula_297, yields Thus, the magnitude of a point formula_313 in the direction formula_297 on the inertia ellipsoid is Moment of inertia The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a tensor that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to title: Moment of inertia text: an extended body of a regular shape and uniform density, this summation sometimes produces a simple expression that depends on the dimensions, shape and total mass of the object. In 1673 Christiaan Huygens introduced this parameter in his study of the oscillation of a body hanging from a pivot, known as a compound pendulum. The term "moment of inertia" was introduced by Leonhard Euler in his book "Theoria motus corporum solidorum seu rigidorum" in 1765, and it is incorporated into Euler's second law. The natural frequency of oscillation of a compound pendulum is obtained from the ratio of the torque title: Statics text: moment,rotational inertia, polar moment of inertia of mass, or the angular mass, (SI units kg·m²) is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation. The moment of inertia plays much the same role in rotational dynamics as mass does in linear dynamics, describing the relationship between angular momentum and angular velocity, torque and angular acceleration, and several other quantities. The symbols I and J are usually used to refer to the moment of inertia or polar moment of inertia. While a simple scalar treatment title: Moment of inertia text: is diagonal and torques around the axes act independently of each other. When a body is free to rotate around an axis, torque must be applied to change its angular momentum. The amount of torque needed to cause any given angular acceleration (the rate of change in angular velocity) is proportional to the moment of inertia of the body. Moment of inertia may be expressed in units of kilogram meter squared (kg·m) in SI units and pound-foot-second squared (lbf·ft·s) in imperial or US units. Moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics