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 particle moves around the origin in a circle; but when there is no cross-radial component, it moves in a straight line from the origin. Since radial motion leaves the angle unchanged, only the cross-radial component of linear velocity contributes to angular velocity. The angular velocity "ω" is the rate of change of angle with respect to time, which can be computed from the cross-radial velocity as: Here the cross-radial speed formula_13 is the signed magnitude of formula_11, positive for counter-clockwise motion, negative for clockwise. Taking polar coordinates for the linear velocity v gives magnitude "v" (linear speed) and angle "θ"