When a skater is spinning with arms and free leg extended, the moment of inertia

Question

When a skater is spinning with arms and free leg extended, the moment of inertia is 12 kgm^2. When the same skater brings both arms and free leg in close to the axis of rotation, the moment of inertia is 4.5 kgm^2. If the initial angular speed with arms and free leg extended is 3.5 rad/s, what is the angular velocity after the arms and free leg are brought in close to the axis of rotation? Mow much work docs the skater do while moving the arms and free leg from the extended position to the close to the axis position?

Explanation / Answer

as there is no net external force applied so angular momentum of system will be conserved

I1*w1 = I2 * w2

12*3.5 = 4.5 * w2

w2 = 9.33333333333 rad/s

work done = change in kinetic energy

0.5 I2 W2 ^2 - 0.5 * I1 * W1 ^2

0.5*4.5*9.33^2 - 0.5* 12 *3.5^2

122.360025 Joules

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