Moment of inertia 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
Linear elasticity fourth-order stiffness tensor, formula_8 is the body force per unit volume, formula_9 is the mass density, formula_10 represents the nabla operator, formula_11 represents a transpose, formula_12 represents the second derivative with respect to time, and formula_13 is the inner product of two second-order tensors (summation over repeated indices is implied). Expressed in terms of components with respect to a rectangular Cartesian coordinate system, the governing equations of linear elasticity are: An elastostatic boundary value problem for an isotropic-homogeneous media is a system of 15 independent equations and equal number of unknowns (3 equilibrium equations, 6 strain-displacement equations, and 6 constitutive