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 is formula_5, and the linear velocity is formula_6, so that formula_7. In the general case of a particle moving in the plane, the angular velocity is measured relative to a chosen center point, called the origin. The diagram shows the radius vector r from the origin "O" to the particle "P", with its polar coordinates formula_8. (All variables are functions of time "t".) The particle has linear velocity splitting as formula_9, with the radial component formula_10 parallel to the radius, and the cross-radial (or tangential or circular) component formula_11 perpendicular to the radius. When there is no radial component, the