Question

A skater on ice with arms extended and one leg out spins at 3 rev/s. After he draws his arms and the leg in, his moment of inertia is reduced to 1/2. What is his new angular speed

Answer 1

Answer:

The new angular speed is $w = 6 \ rev/s$

Explanation:

From the  question we are told that

      The angular velocity of the spin is  $w_o = 3 \ rev/s$

       The  original moment of inertia is  $I_o$

        The new moment of inertia is  $I =\frac{I_o}{2}$    

Generally angular momentum is mathematically represented as

      $L = I * w$

Now according to the law of conservation of momentum, the initial momentum is equal to the final momentum hence the angular momentum is constant so

         $I * w = constant$

=>       $I_o * w _o = I * w$

where w is the new angular speed  

  So  

          $I_o * 3 = \frac{I_o}{2} * w$

=>        $w = \frac{3 * I_o}{\frac{I_o}{2} }$

=>         $w = 6 \ rev/s$