Physics Torque Question?

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Dan P

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Starting from rest, a 12-cm-diameter compact disk takes 3.0 s to reach its operating angular velocity of 2000 rpm. Assume that the angular acceleration is constant. The disk's moment of inertia is 2. x10 ^-5 kg m^2.

How much torque is applied to the disk?

How many revolutions does it make before reaching full speed?
 
T = Iα
wf = (2000 rev/min)*(2pi rad / 1 rev)*(1 min / 60 s) = 209 rad/s
wf = wi + αt -- wi = 0 so the equation simplifies to
wf = αt
α = wf/t = (209 rad/s) / 3 s = 70 rad/s^2
T = Iα = (2*10^-5 kg m^2)*(70 rad/s^2) = 1.4*10^-3 N*m

θf = θi t + 1/2 αt^2
θf = 1/2 αt^2 = 1/2 (70 rad/s^2)(3 s)^2 = 315 rad
(315 rad)*(1 rev / 2pi rad) = 50 rev
 
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