Grinding Wheel

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Frequently Asked Questions...

How long does a grinding wheel take to reach twice this angular velocity in this problem?

a grinding wheel is span up to a speed by a motor that produces a constant power it takes time to reach angular velocity assuming negligible friction at the axle, how long does it take to reach twice this angular velocity?

Please help :[

thanks:]


Answer:

  The angular velocity = dθ/dt

  Rotational Kinetic Energy = KEʀ is proportional to [dθ/dt]²

 Therefore it takes 4× the energy to reach 2[dθ/dt] compared to the energy
 it takes to reach dθ/dt

 Since power is constant then energy increases linearly with time. So it takes 4×
 as long to reach 2[dθ/dt] compared to the time it takes to reach dθ/dt

  KEʀ for 2[dθ/dt] = (4 × KEʀ) for [dθ/dt]

  time for 2[dθ/dt] = (4 × time) for [dθ/dt]

** but the additional time it takes is 4× − 1× = 3× the time it took to reach dθ/dt
 Example: If it takes 3 sec to reach dθ/dt then it will take 9 additional sec to
      reach 2[dθ/dt] or a total of 12 sec to reach 2[dθ/dt]

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Grinding Wheel

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