Angular impulse

If angular momentum is the analogue of momentum, then there must also be an analogue of impulse: the quantity describing how much angular momentum is transferred. This is angular impulse.

Principle — Angular impulse

The exchange of angular momentum between two systems takes place through angular impulse. For a constant moment: $I_\text{ang} = M\cdot\Delta t$ In general, a force $\vec{F}$ applied for a time $\Delta t$ at a point at distance $\vec{r}$ from the pole produces: $\vec{I}_\text{ang} = \vec{r}\times(\vec{F}\,\Delta t) = \vec{r}\times\vec{I}$

The formula mirrors perfectly the translational impulse theorem $\vec{I} = \vec{F}\,\Delta t = \Delta\vec{p}$: here the angular impulse equals the change in angular momentum, $\vec{I}_\text{ang} = \Delta\vec{L}$. The presence of the cross product $\vec{r}\times\vec{I}$ reminds us that what matters is not only how much linear impulse is given, but also where and in which direction: the same impulse $\vec{I}$ applied far from the pole transfers more angular momentum than when applied close to it.

This is why, to make a door swing quickly, you push it as far as possible from the hinges: for the same force and duration, the larger arm maximises the angular impulse transmitted. Applying the same push near the hinges is nearly useless.

Collegamenti

Argomenti: Dinamica rotazionale Concetti: Momento angolare · Conservazione del momento angolare

Esercizi collegati: Il tuffatore che ruota · Cometa al perielio e all’afelio · Problema — Momento torcente rettangolare e L(t)