A spinning disc rotating at 130 rev/min slows and stops 31 s later. how many revolutions did the disc make during this time?

F = 130 revs/min = 130/60 revs/s = 13/6 revs/s

t = 31s

wi = 2πf = 2π * 13/6 = 13π/3 rads/s

wf = 0 rads/s = wi + at

a = - wi/t = - 13π/3 * 1/31 = - 13π/93 rads/s²

wf² - wi² = 2a∅

-169π²/9 rads²/s² = 2 * - 13π/93 rads/s² * ∅

∅ = 1209π/18 rads

n = ∅/2π = (1209π/18) / (2π) = 1209/36 ≈ 33.5833 revolutions.