Problem: A computer disk drive is turned on starting from rest and has a constant angular acceleration. If it took 0.0865 s for the drive to make its second revolution, (a) how long did it take to make the first complete revolution, and (b) what is its angular acceleration, in rad/s2?

FREE Expert Solution

Rotational kinematic equations:

ω = ω0 + αtθ = ω0t + 12αt2ω2 = ω02 + 2αθ

For the first round:

  • t1 = t s
  • θ1 = 2π
  • ω0 = 0 rad/s
  • α1 = α (constant)
  • ω1 = ?

For the second round:

  • t2 = (t + 0.0865) s
  • θ2 = 4π rad
  • ω0 = 0 rad/s
  • α2 = α (constant)
  • ω2 = ?

(a)

We need an expression that does not have ω (ω1, ω2):

θ1 = ω0t1 + (1/2)αt12 

2π = 0 + (1/2)(α)(t2)  Equation 1

θ2 = ω0t2 + (1/2)αt22 

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Problem Details

A computer disk drive is turned on starting from rest and has a constant angular acceleration. If it took 0.0865 s for the drive to make its second revolution, 

(a) how long did it take to make the first complete revolution, and 

(b) what is its angular acceleration, in rad/s2?

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