Acomputer hard disk starts from rest, then speeds up with an angular acceleration of 190 rad/s2 until it reaches its final angular speed of 7200 rpm. part a how many revolutions has the disk made 10.0 s after it starts up?

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
 
 the disk has made 961.57 rev 10.0 s after it starts up

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