Question

If an ice-skater, with an initial rotational speed of 4.0 radians/s, extends

her arms to increase her rotational inertia to 3/2 its original value, what is her new

rotational velocity?

Answer 1

If there is no external torque applied to the system, the angular momentum of the system remains constant. So, for a rotational motion around an axis, the angular momentum around that axis is
  
   
where, I is the moment of inertia of the system around that axis and \omega is the angular velocity of the system. Now if the moment of inertia increases then from above equation, in order to keep the angular momentum L to be constant, the angular velocity \omega decreases. i.e,
  
  
And so,
   As given
     
so, we get
  

Now if , then, the new angular velocity is