A) The star's moment of inertia I has decreased, and its angular momentum L has increased
B) The star's moment of inertia I has decreased, and its angular velocity \[\omega \] has decreased
C) The star's moment of inertia I remains constant, and its angular momentum L has increased
D) The star's angular momentum L remains constant, and its rotational kinetic energy has increased
Correct Answer: D
Solution :
| According to conservation of angular momentum, the angular momentum L of the star remains constant, so when its moment of inertia I increase (due to the decreased radius), its angular velocity w goes up proportionally, according to: |
| \[{{L}_{initial}}={{L}_{final}}\] |
| \[{{I}_{i}}{{\omega }_{i}}={{I}_{f}}{{\omega }_{f}}\] |
| \[\omega f=\frac{{{I}_{i}}}{{{I}_{f}}}{{\omega }_{i}}\] |
| The star?s rotational kinetic energy, based on \[{{K}_{rotational}}=\frac{1}{2}I{{\omega }^{2}}\] also goes up. Although I has decreased, \[{{K}_{rotational}}\] increases with the square of w, leading to net increase in energy. |
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