Euler’s second law: torques and angular momentum
In this post, I explore Euler’s Second Law to show how torques influence the angular momentum in systems of particles and rigid bodies. Using Newton’s Second Law as a starting point:
\sum \mathbf{F} = \frac{\mathrm d\mathbf{p}}{\mathrm dt}
I extend this principle to rotational dynamics, deriving the moment of force (torque) equation:
\sum \mathbf{M}_O = \frac{\mathrm d\mathbf{L}_O}{\mathrm dt}
Here, \mathbf{M}_O represents the net torque about a fixed point O, and \mathbf{L}_O is the angular momentum about that point. I also present how angular momentum can be expressed relative to an arbitrary point, such as the center of mass, and its relation to the system’s linear momentum.
By applying these equations, I demonstrate their utility in analyzing the dynamic behavior of systems, bridging linear and angular motion effectively. These formulations offer powerful tools for understanding mechanical systems in advanced studies.
For more insights into this topic, you can find the details here.