Question

A figure skater rotating at 5.93 rad/s with arms extended has a moment of inertia of 2.40 kgm². If the arms are pulled in so the moment of inertia decreases to 1.81 kgm², what is the final angular speed? Express your answer in rad/s to two decimal places.

Answer 1

Given
   skater initial angular speed w1 = 5.93 rad/s, moment of inertia when arms extended I1 = 2.40 kgm2

   skater fiial angular speed w2 = ? rad/s, moment of inertia when arms pulled in I2 = 1.81 kgm2

conservation of angular momentum is L = I*W, L1=L2

               I1*W1 = I2*W2
               W2 =(I1*W1/I2) rad/s
               W2 = (2.40*5.93/1.81) rad/s
               W2 = 7.86 rad/s

so the angular speed when the skater pulled in the arms is W2 = 7.86 rad/s