A spinning disk with 130 rev/min will make 33.5833 revolutions in 31 seconds.
Initial angular velocity,
wi = 2π. f
Where, f - frequency = 130 rev/min = 13/6 rev/s
Thus,
wi = 2π × 13/6
wi = 13π/3 rads/s
Final angular velocity,
wf = 0 rads/s = wi + at
From acceleration,
a = -wi/t
Where,
a - acceleration
t - time = 31s
So,
t = -13π/3 × 1/31
t = -13π/93 rads/s²
From relation between Tangential velocity and Angular velocity,
wf² - wi² = 2a∅
Where, ∅ is the Tangential velocity
Thus,
-169π²/9 rads²/s² = 2 × -13π/93 rads/s² × ∅
∅ = 1209π/18 rads
Thus, the the number of rotations,
n = ∅/2π
n = (1209π/18)/(2π)
n = 1209/36
n = ≈ 33.5833 revolutions.
Therefore, the disc make 33.5833 revolutions in 31 seconds.
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