Section 5.22 Conservation Analysis
You have previously used two conservation laws:
The Work-Energy Theorem and
The Impulse-Momentum Theorem. The work-energy theorem already includes rotational kinetic energy, but the impulse-momentum theorem is purely translational. You can, however, define an angular analogue for it
1 .
Principle 5.22.1. Conservation of Angular Momentum (The Angular Impulse-Momentum Theorem).
The net angular impulse delivered to a system is equal to the change in angular momentum for that system:
\begin{equation*}
\vec{\tau}_{net}\Delta t = \Delta \vec{L}
\end{equation*}
Even though this expression looks very similar to the impulse-momentum theorem, it is entirely separate! This suggests that angular momentum can be conserved (or not conserved) independent of whether translational momentum is conserved (or not). Additionally, translational momentum can never be converted into angular momentum (though the same thing is not true for translational and angular kinetic energy).
Exercises Activities
1.
What is the condition that must be met for the angular momentum of a system to be conserved?
Answer.If angular momentum is conserved then \(\Delta \vec{L} = 0\text{;}\) this can only be true if \(\vec{\tau}_{net} = 0\) as well.
2.
Visit
this link and watch the video. Be sure to make and record your prediction and watch the following videos to see what happens!
3.
Once you have watched the videos, write a brief (1-2 sentence) summary of what you learned from them.
References References
[1]
The Bullet Block Experiment by Veritasium.
you could imagine calling this the Angular-Impulse-Momentum theorem, which is wordy, but most physicists talk about it as Conservation of Angular Momentum, even in situations where the angular momentum is not in fact conserved
