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
Reduced mass a multitude of two-body problems, where classical mechanics is applicable. In a system with two point masses m and m such that they are co-linear, the center of mass may be found via formula_25. The moment of inertia of this system in the center of mass frame of reference is a two-body problem with two masses, each with its own distance to the center of mass. By converting to the equivalent reduced mass frame of reference, the system may be treated as a single reduced mass, μ, with a distance, d, equal to the sum of x and x. This