Answer:
50
Explanation:
ωo = 0, t = 8 s, f = 5 rev/s, ω = 2 x 3.14 x f = 2 x 3.14 x 5 = 31.4 rad/s
Initially when the washer is accelerating
Let α be the angular acceleration
ω = ωo + α t
31.4 = 0 + α x 8
α = 3.925 rad/s^2
Let the number of revolutions be θ.
θ = ωo x t + 1/2 α x t^2
θ = 0 + 0.5 x 3.935 x 8 x 8 = 125.6 rad
Number of revolutions, n1 = θ / 2π = 125.6 / (2 x 3.14) = 20 revolutions
When the washer is switch off
ω = 0, t = 12 s, ωo = 31.4 rad/s
Let α be the angular acceleration
ω = ωo + α t
0 = 31.4 + α x 12
α = - 2.62 rad/s^2
Let the number of revolutions be θ.
θ = ωo x t + 1/2 α x t^2
θ = 31.4 x 12 - 0.5 x 2.62 x 12 x 12 = 188.16 rad
Number of revolutions, n2 = θ / 2π = 188.16 / (2 x 3.14) = 30 revolutions
Total number of revolutions, n = n1 + n2 = 20 + 30 = 50
