Translated, it’s something per unit time per unit time. If this something is the change in length then it’s linear acceleration (a). If it is a pure number then it is angular acceleration (a). These two concepts are related by a = ar, where r is the radius of circular motion. Both described different aspect of uniform motion.

In classical physics, linear inertial acceleration is directly proportional to inertial force (F) but inversely proportional to inertial mass (m). However, in classical general relativity, acceleration is directly proportional to dark energy and power of distance. This is determined by Hubble law for the Doppler effect of galactic redshifts. Recently, a surprising discovery was made by two independent groups (1) Supernova Cosmology Project at Caltech’s Lawrence Berkeley Lab and (2) High-z Supernova Team (an international consortium). They were hoping to measure galactic distances more accurately by replacing Cepheid variables with Type Ia supernovae. What they found is that the light from older Type Ia’s appeared brighter (less redshifted) than younger Type Ia’s. This is an indication that closer ones are accelerating faster now than that of the old ones at farther distances.

Although angular acceleration is a vector quantity, it is not clear just how to represent its direction except by the conventional right hand rule conformed by the definition of a torque. Furthermore, torque (t) as product of moment of inertia (I) and angular acceleration (a) is analogous to Newton’s second law of motion F = ma. However, a = 2p c/DlDt, where c is the constant of light speed, Dlis the change in wavelength, and Dt is the change in time. Therefore, linear acceleration is a = 2p r c/DlDt, where 2p r is the circumference of the visible universe and a =cC/DlDt. The Hubble law is that the velocity of recession (v) is equal to the product of Hubble constant (H) and separation of galaxies (L), v = HL. Taking the derivative of v gives the acceleration a = H(dL/dt) = caC/Dl.