The first thing we are going to do is find the equation of motion:
ωf = ωi + αt
θ = ωi*t + 1/2αt^2
Where:
ωf = final angular velocity
ωi = initial angular velocity
α = Angular acceleration
θ = Revolutions.
t = time.
We have then:
ωf = (7200) * ((2 * pi) / 60) = 753.60 rad / s
ωi = 0
α = 190 rad / s2
Clearing t:
753.60 = 0 + 190*t
t = 753.60 / 190
t = 3.97 s
Then, replacing the time:
θ1 = 0 + (1/2) * (190) * (3.97) ^ 2
θ1 = 1494.51 rad
For (10-3.97) s:
θ2 = ωf * t
θ2 = (753.60 rad / s) * (10-3.97) s
θ2 = 4544,208 rad
Number of final revolutions:
θ1 + θ2 = (1494.51 rad + 4544.208 rad) * (180 / π)
θ1 + θ2 = 961.57 rev
Answer:
the disk has made 961.57 rev 10.0 s after it starts up
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