Mass (say) 1 kilogram. Then we can measure the mass of any other object in the universe by colliding it with the reference object and measuring the accelerations. Additionally, mass relates a body's momentum p to its linear velocity v: and the body's kinetic energy "K" to its velocity: The primary difficulty with Mach's definition of mass is that it fails to take into account the potential energy (or binding energy) needed to bring two masses sufficiently close to one another to perform the measurement of mass. This is most vividly demonstrated by comparing the mass of the proton in the
Angular velocity origin: The relation between this linear map and the angular velocity pseudovector formula_74 is the following. Because "W" is the derivative of an orthogonal transformation, the bilinear form is skew-symmetric. Thus we can apply the fact of exterior algebra that there is a unique linear form formula_76 on formula_77 that where formula_79 is the exterior product of formula_80 and formula_81. Taking the sharp "L" of "L" we get Introducing formula_83, as the Hodge dual of "L", and applying the definition of the Hodge dual twice supposing that the preferred unit 3-vector is formula_84 where by definition. Because formula_81 is an