A figure skater is spinning with her arms out wide. Will she spin faster or slower if she tucks in her arms? Why?
She has increased her moment of inertia.
Angular momentum is conserved;
angular momentum = inertia*angular velocity
if inertia is increased, angular velocity....
To understand whether a figure skater will spin faster or slower when she tucks in her arms, let's consider the principle of conservation of angular momentum.
Angular momentum is a property of rotating objects and depends on two factors: inertia and rotational speed. When the skater's arms are extended, they contribute to her overall moment of inertia, which is the measure of an object's resistance to changes in rotation. By tucking in her arms, she reduces her moment of inertia.
According to the conservation of angular momentum, the total angular momentum of a system remains constant unless acted upon by an external torque. If the skater reduces her moment of inertia by tucking in her arms, her angular momentum must be conserved by increasing her rotational speed.
Therefore, the skater will spin faster when she tucks in her arms because reducing her moment of inertia allows her to concentrate her mass closer to her center of rotation, enabling her to spin more rapidly.