Physics
Mechanics
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Question

A man of mass 100 kg stands at the rim of a turn table of radius 2m, moment of inertia 4000 kg. The table is mounted on a vertical smooth axis, through its center. The whole system is initially at rest. The man now walks on table with a velocity 1 m/s relative to earth
Through what angle will it have rotated when the man reaches his initial position relative to earth

  1. pi over 5 rad divided by sec
  2. fraction numerator 2 pi over denominator 5 end fraction rad divided by sec
  3. fraction numerator 2 pi over denominator 11 end fraction r a d divided by sec
  4. pi over 11 rad divided by sec

The correct answer is: pi over 5 rad divided by sec


    text  If the man completes one revolution relative to the earth, then  end text theta subscript m equals 2 pi
text  Time  end text equals fraction numerator 2 pi over denominator omega subscript m end fraction equals fraction numerator 2 pi over denominator 0.5 end fraction
D u r i n g space t h i s space t i m e comma space a n g u l a r space d i s p l a c e m e n t space o n space t h e space t a b l e comma
table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row cell theta subscript t equals omega subscript 1 left parenthesis text  time  end text right parenthesis equals negative 0.05 cross times fraction numerator 2 pi over denominator 0.5 end fraction end cell row cell equals negative pi over 5 text  radian  end text comma theta subscript t equals 36 to the power of ring operator text  in clockwise direction  end text end cell end table

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