Discussion
Let \(\vec{r}\), \(\vec{V}\), and \(m\) be position vector, velocity vector, and mass, respectively in a control mass system. Which one of the following properties is considered as conserved extensive property in Reynolds Transport Theorem to obtain the angular momentum equation?
Answer: A
The extensive property is the angular momentum \(\vec{r} \times m\vec{V}\).
The Reynolds Transport Theorem converts the rate of change of any extensive property B of a system into control-volume terms. Choosing \(B = \vec{r} \times m\vec{V}\), the moment of momentum, with its intensive form \(b = \vec{r} \times \vec{V}\), gives the angular momentum equation, whose system-level statement is that the net torque equals the rate of change of angular momentum.
\(\vec{r} \times \vec{V}\) is the intensive (per unit mass) form, not the extensive property. \(m\vec{V}\) gives the linear momentum equation and \(m\) gives continuity.
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