Living Force

Living force, or kinetic energy, is the product of the mass of a moving body m and half the square of its velocity v, i.e. -_a- By expending some work W, one can slow down or, conversely, accelerate the motion of a body, changing its velocity from v₁ to v₂. According to the laws of mechanics, in such a case: mv₁²/2 - mv₂²/2 = W, i.e. the increase (or decrease) of living force equals the expended (or obtained) work. This constitutes the so-called theorem of living force, representing a particular case of the law of conservation of energy. The living force of a solid body rotating around a certain axis is expressed by the formula -- Here J is the moment of inertia of the body relative to the given axis of rotation, i.e. the sum of the products of the masses of individual points of the body by the square of their distance r from the axis of rotation: J=Σmr²; and ω is the angular velocity, i.e. the quotient of dividing the linear velocity v of a given point by r: ω=v/r. If any reserve of energy is completely explained by the movements of material points, then the energy can rightfully be called kinetic*. For example, heat is completely explained by the translational and rotational movements of the molecules of a body, and therefore thermal energy is kinetic.