Physics
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
With what angular velocity will the turn table rotate

  1. 0.5 rad/sec 
  2. 0.1 rad/sec
  3. 0.05 rad/sec 
  4. 0.2 rad/sec

The correct answer is: 0.05 rad/sec


    By conservation of angular momentum on the man table system,
    table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell L with not stretchy rightwards arrow on top subscript i equals L with not stretchy rightwards arrow on top subscript f text  or  end text 0 plus 0 equals I subscript m omega subscript m plus I subscript t omega subscript t end cell row cell omega subscript t equals negative fraction numerator I subscript m omega subscript m over denominator I subscript 1 end fraction text  where  end text omega subscript m equals v over r equals 1 half r a d divided by s end cell row cell omega subscript t equals negative 100 left parenthesis 2 right parenthesis squared cross times fraction numerator 1 divided by 2 over denominator 4000 end fraction equals negative 1 over 20 rad divided by straight s end cell end table
    Thus the table rotates clockwise (opposite to man) with angular velocity 0.05 rad/s.

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