A figure skater spinning in a circle and dazzling the Olympic judges brings her arms together for a final flourish.
1. Does her angular momentum increase, decrease, or stay the same after she pulls her arm in?
2. Does her angular velocity increase, decrease, or stay the same after she pulls her arms in?
3. Does her angular acceleration increase, decrease, or stay the same after she pulls her arms in?
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.
1. When the figure skater pulls her arms in, her angular momentum decreases. According to the conservation of angular momentum, when the moment of inertia decreases (which happens when she pulls her arms in), the angular velocity must increase proportionally to maintain the same amount of angular momentum. Therefore, as her arms come closer to her body, her moment of inertia decreases, resulting in a decrease in angular momentum.
2. After pulling her arms in, the figure skater's angular velocity increases. This is because of the conservation of angular momentum, as mentioned before. As the moment of inertia decreases when she pulls her arms in, her angular velocity must increase to maintain the same amount of angular momentum.
3. The figure skater's angular acceleration does not change when she pulls her arms in. Angular acceleration is related to the torque applied to an object and is independent of the moment of inertia or angular velocity. Therefore, the act of pulling her arms in does not affect her angular acceleration.