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Since angular acceleration is in radians per second squared, which is change in angular speed over time, we know that α=ω/t, where α is angular acceleration, ω is angular speed, and t is time (assuming α is constant.)
ω is measured in radians per second. If me multiply ω by r, which is the radius of the circle the object is acceleration around, we get ωr, which has units of (radians*radius)/second. Since the angle in radians times the radius gives the distance, these units are equivalent to meters/second, so ωr = v.
Therefore, α=(v/r)/t=v/rt.
Acceleration (a) is v/t, so α=(v/t)(1/r)=a/r.
The equation would then be:
α=a/r, or a=rα (Where α is angular acceleration, a is acceleration, and r is the radius.)
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