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A disk with a moment of inertia of 60+1.5 kgm2 rotates at a speed of of...

A disk with a moment of inertia of 60+1.5 kgm2 rotates at a speed of of 56+5 radians/sec. Calculate the uncertainty in the kinetic energy. Include units.

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Answer #1

given
disk with moment of inertia I = 60+1.5 kg.m^2

roating with a speed of w = 56+5 radian /sec

we know that the rotational kinetic energy is k.e_r = 0.5* I*W^2

   k.e_r = 0.5*60*56^2 J

   k.e_r = 9.4080*10^4 J


now the uncertainity in kinetic energy is given by

   dK.e_r = k.e_r (dI/I)+2(dw/w)

   dk.e_r = (94080)(1.5/60)+2(5/56) J
  
   dk.e_r = 0.235218*10^4 J


so the uncertainity in the kinetic energy is k = (9.4080+-0.235218)*10^4 J

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