A diffuse, uniformly rotating interstellar gas cloud has mass and an initial radius…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

A diffuse, uniformly rotating interstellar gas cloud has mass

2.0\times10^{30}\,\text{kg}

and an initial radius of

1.0\times10^{12}\,\text{m}

. The cloud completes one full rotation every

1.0\times10^{6}\,\text{yr}

. Over time it contracts to form a protostar of radius

5.0\times10^{8}\,\text{m}

. Treat the cloud and the final protostar as uniform solid spheres and ignore any external torques during the contraction. (a) Determine the initial angular speed of the cloud. (b) Calculate the angular speed of the protostar immediately after the contraction is complete. (c) Find the new rotation period of the protostar in hours. (d) Compute the ratio of the final to the initial rotational kinetic energies, and discuss qualitatively where the difference in energy could have gone or come from during the contraction.

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