I\'m not so sure on how to get started on this question. Thereis no sample solut

Question

I'm not so sure on how to get started on this question. Thereis no sample solution available and it looks like an EpertQuestion. But still I would like to be guided on how to solve it. Ikeep thinking of using the Rotationa kinetic energy equation butthen I've got a given torque and a distance of string 8.0cm. I'mnot sure how to solve this. The top has a moment of inertia of 4.00 x10-4 kgm2 and is initially at rest. Itis free to rotate about the stationary axis AA'. A string,wrapped around a peg along the axis of the top, is pulled in such amanner as to maintain a constant tension of 5.57 N. If the string does not slip while it isunwound from the peg, what is the angular speed of the top after80.0 cm of string has been pulled off the peg? I'm not so sure on how to get started on this question. Thereis no sample solution available and it looks like an EpertQuestion. But still I would like to be guided on how to solve it. Ikeep thinking of using the Rotationa kinetic energy equation butthen I've got a given torque and a distance of string 8.0cm. I'mnot sure how to solve this.

Explanation / Answer

   Tension F = 5.57 N
   Moment of inertia of thetop I = 4.00 x 10-4kg .m2    Distance to which thestring is pulled off d = 80 cm                                                                   =0.80 m    Distance to which thestring is pulled off d = 80 cm                                                                   =0.80 m    The total work done isgiven by
   W = F d
       = (5.57N) (0.8m)         = 4.46 J
   Using the work-kinetic energy theroem weget
   W = KE         =(1 / 2) I f2 - (1 / 2) Ii2    As the top starts fromrest i = 0    So then we get
   W = (1 / 2) I f2
   4.46 J = (1 / 2) I f2    4.46 J = (1 / 2) (4.00 x 10-4kg . m2) f2    so theangular speed of the top after 80.0 cm of string has beenpulled off the peg will be    f = 148.68 rad / s    4.46 J = (1 / 2) (4.00 x 10-4kg . m2) f2    so theangular speed of the top after 80.0 cm of string has beenpulled off the peg will be    f = 148.68 rad / s    so theangular speed of the top after 80.0 cm of string has beenpulled off the peg will be

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