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
Rigid body its position and orientation vary with time. In the kinematic sense, these changes are referred to as "translation" and "rotation", respectively. Indeed, the position of a rigid body can be viewed as a hypothetic translation and rotation (roto-translation) of the body starting from a hypothetic reference position (not necessarily coinciding with a position actually taken by the body during its motion). Velocity (also called linear velocity) and angular velocity are measured with respect to a frame of reference. The linear velocity of a rigid body is a vector quantity, equal to the time rate of change of its linear position.