Question

3.3.2 test (cst): forces
question 19 of 20
the photo shows a pair of figure skaters performing a spin maneuver. the axis of rotation goes through the left foot of the skater on the left. what action could decrease their angular velocity?
a. the skater on the left allows the distance between the pair to increase.
b. the skater on the left points his right arm down instead of up.
c. the skater on the left pulls the skater on the right closer to him.
d. the skater on the right points her head upward instead of downward.
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Explanation:

Step1: Recall the law of conservation of angular momentum

The law of conservation of angular momentum states that \(L = I\omega\) (where \(L\) is angular momentum, \(I\) is moment of inertia, and \(\omega\) is angular velocity). In the absence of external torques, \(L\) is constant. So, \(\omega=\frac{L}{I}\). To decrease \(\omega\), we need to increase \(I\).

Step2: Analyze the moment of inertia formula

The moment of inertia \(I = \sum_{i}m_{i}r_{i}^{2}\) (for a system of particles). Increasing the distance \(r\) of the mass from the axis of rotation increases \(I\).

Step3: Evaluate each option

• Option A: If the skater on the left allows the distance between the pair to increase, the moment of inertia \(I\) of the system (since the skater on the right is further from the axis of rotation) increases. Using \(\omega=\frac{L}{I}\) (\(L\) is constant as there are no external torques on the system), \(\omega\) decreases.
• Option B: The skater on the left pointing his right - arm down instead of up has a negligible effect on the overall moment of inertia of the system (as the mass of the arm is small compared to the total mass of the system and the change in its position relative to the axis of rotation is not significant enough to cause a large change in \(I\)).
• Option C: Pulling the skater on the right closer to the axis of rotation decreases the moment of inertia \(I\) (since \(r\) for the skater on the right decreases). Using \(\omega=\frac{L}{I}\), \(\omega\) would increase.
• Option D: The skater on the right pointing her head upward instead of downward has a negligible effect on the moment of inertia (as the mass of the head is a very small fraction of the total mass of the system and the change in its position relative to the axis of rotation is minimal).

Answer:

A. The skater on the left allows the distance between the pair to increase.