Question

if a figure skater is spinning around with her arms outstretched, why will she spin faster if she brings her arms in?
by bringing in her arms she is reducing the air drag on her and hence, she spins faster.
energy is always conserved. by bringing her arms in she is decreasing her pe. to keep her total energy constant her ke must increase. hence, she spins faster.
momentum is always conserved. by bringing her arms in she is decreasing her mass. with less mass, in order to keep her momentum constant she must spin faster.
angular momentum is always conserved. by bringing her arms in she is decreasing her radius. in order to keep her angular momentum from changing, she must spin faster.

Explanation:

• Option 1: Air drag is not the main reason. The change in rotational speed is mainly related to rotational mechanics, not air drag.
• Option 2: While energy conservation is a principle, in this case, it's angular momentum (not just total energy in the simple KE - PE sense for this rotational situation) that is directly relevant.
• Option 3: Mass of the skater does not change when she brings her arms in.
• Option 4: According to the law of conservation of angular momentum \(L = I\omega\) (where \(I\) is the moment of inertia and \(\omega\) is the angular velocity). When she brings her arms in, the moment of inertia \(I=\sum m_ir_i^2\) (sum over the mass elements \(m_i\) and their distances \(r_i\) from the axis of rotation) decreases. Since \(L\) is conserved (\(L = constant\)), if \(I\) decreases, \(\omega\) (angular speed) must increase.

Answer:

Angular momentum is always conserved. By bringing her arms in she is decreasing her radius. In order to keep her angular momentum from changing, she must spin faster.