Question

if the moment of inertia of a figure skater about some vertical axis increases by 20% and her angular speed about the same axis decreases by 10%, what would happen to her angular momentum as measured about the same axis?

Answer 1

The skater's angular momentum remains the same because angular momentum is conserved when no external torques are present, despite changes in moment of inertia and angular velocity.

Step-by-step explanation:

If the moment of inertia of a figure skater about some vertical axis increases by 20% and her angular speed about the same axis decreases by 10%, the skater's angular momentum about the axis would remain the same. This is because angular momentum is conserved when no external torques act on the system, which is a principle known as the conservation of angular momentum.

Although there is a change in the moment of inertia and angular velocity, these changes are inversely proportional, meaning the overall angular momentum does not change.

Answer 2

The figure skater's angular momentum remains constant when the moment of inertia increases by 20% and angular speed decreases by 10%. This is a result of the conservation of angular momentum, assuming no external torques act upon the skater.

Step-by-step explanation:

If the moment of inertia of a figure skater about a vertical axis increases by 20% and her angular speed about the same axis decreases by 10%, the skater's angular momentum about the axis remains constant. This is due to the conservation of angular momentum, which states that if no external torques are acting on a system, the total angular momentum will not change. In the case of a figure skater spinning on ice, the net external torque is typically negligible due to the low friction between the skates and the ice.

Therefore, an increase in moment of inertia coupled with a decrease in angular velocity would still result in the same total angular momentum for the skater. This principle is often seen when figure skaters pull their arms in to spin faster; the work done to pull in the arms converts to an increase in rotational kinetic energy, but the angular momentum remains constant as long as no external torques act on the system.