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Mechanics
Easy

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 the turn table have rotated when the man reaches his initial position on it

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

The correct answer is: pi over 11 r a d divided by sec


    text  If the man completes one revolution relative to the table then  end text theta subscript m t end subscript equals 2 pi semicolon 2 pi equals theta subscript m minus theta subscript t
2 pi equals omega subscript m t minus omega subscript t t space of 1em text  (where tis the time taken)  end text
text  Angular displacement of table is  end text
theta subscript t equals omega subscript t t equals negative 5.05 cross times left parenthesis 2 pi divided by 0.55 right parenthesis equals negative fraction numerator 2 pi over denominator 11 end fraction radian

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