Question

An ice skater quickly extends his arms when he turns on himself. Will its kinetic energy be conserved? Will your mechanical energy be conserved? Will its angular momentum be conserved? (Disregard the friction in the time interval that two it takes to extend the arms.) If any of these magnitudes is not preserved tell whether it increases or decreases.

Answer 1

only angular momentum is conserved The angular momentum L=Iω constant when neglecting friction as there is no external torque. As the moment of inertia I decreases due to the skater pulling her arms in, the angular velocity ω increases. But the rotational kinetic energy is E=12Iω^2 So the rotational velocity increases by the same proportion that the moment of inertia decreases, and this increase is squared when calculating the rotational energy.mechanical energy in which kinetic energy is a part of so mechanical energy is not conserved as kinetic energy is not conserved.