Problem — Reading a flat L(t) graph

Problem

The graph shows $L(t)$ of an isolated system: the curve is a horizontal line for all time. What does this mean? What happens to the internal parts?

Solution

$L(t)$ constant means $\dfrac{dL}{dt} = 0$, i.e. the total external torque is zero: the system is isolated from a rotational point of view. Angular momentum is conserved.

Internally, however, things can change: internal forces can redistribute mass and make $I$ and $\omega$ vary separately. What matters is that their product $L = I\omega$ stays fixed. This is exactly what happens with the skater: $I$ and $\omega$ vary, but $L$ traces a perfectly horizontal line. $\ev{L \text{ constant} \Rightarrow \sum M_\text{ext} = 0; \text{ internally } I,\omega \text{ vary, but } I\omega \text{ stays fixed}}$

Links

Topics: Rotational dynamics Concepts: Conservation of angular momentum · Moment of inertia Skills: Reading graphs