To answer these questions, let's break them down one by one:
1. Angular momentum: Angular momentum is a property of a rotating object. It depends on the rotational inertia (moment of inertia) and the angular velocity of the object. The law of conservation of angular momentum states that the angular momentum of a system remains constant unless an external torque is applied.
When the figure skater brings her arms together, she reduces her moment of inertia by bringing the mass closer to the axis of rotation. According to the conservation of angular momentum, if we assume no external torque acts on her, her angular momentum must stay the same. Therefore, her angular momentum remains unchanged when she pulls her arm in.
2. Angular velocity: Angular velocity is the rate of change of angular displacement over time. It represents how fast an object is rotating.
When the skater pulls her arms in, her moment of inertia decreases. By applying the law of conservation of angular momentum, her angular velocity must then increase to compensate for the reduction in moment of inertia. As a result, her angular velocity increases after she pulls her arms in.
3. Angular acceleration: Angular acceleration refers to how fast an object's angular velocity changes over time. It is dependent on the external torque acting on an object.
In this case, we do not have enough information to determine the change in angular acceleration. It depends on whether the skater applies any external torque on herself after pulling her arms in. If she does not apply any external torque, her angular acceleration stays the same. But if she exerts an external torque, her angular acceleration might change accordingly.