The expression for this angular momentum is l → = r → × p →, l → = r → × p →, where the vector r → r → is from the origin to the particle, and p → p → is the particle’s linear momentum. In the preceding section, we introduced the angular momentum of a single particle about a designated origin. In this section, we develop the tools with which we can calculate the total angular momentum of a system of particles. The vector sum of the individual angular momenta give the total angular momentum of the galaxy. The individual stars can be treated as point particles, each of which has its own angular momentum. Consider a spiral galaxy, a rotating island of stars like our own Milky Way. The angular momentum of a system of particles is important in many scientific disciplines, one being astronomy. What is the angular momentum of the proton about the origin? Angular Momentum of a System of Particles The circular path has a radius of 0.4 m and the proton has velocity 4.0 × 10 6 m / s 4.0 × 10 6 m / s. Even if the particle is not rotating about the origin, we can still define an angular momentum in terms of the position vector and the linear momentum.Ī proton spiraling around a magnetic field executes circular motion in the plane of the paper, as shown below. Angular Momentum of a Single Particleįigure 11.9 shows a particle at a position r → r → with linear momentum p → = m v → p → = m v → with respect to the origin. This allows us to develop angular momentum for a system of particles and for a rigid body that is cylindrically symmetric. First, however, we investigate the angular momentum of a single particle. In this chapter, we first define and then explore angular momentum from a variety of viewpoints. Questions like these have answers based in angular momentum, the rotational analog to linear momentum.
Why does Earth keep on spinning? What started it spinning to begin with? Why doesn’t Earth’s gravitational attraction not bring the Moon crashing in toward Earth? And how does an ice skater manage to spin faster and faster simply by pulling her arms in? Why does she not have to exert a torque to spin faster? Use conservation of angular momentum in the analysis of objects that change their rotation rate.Calculate the torque on a rigid body rotating about a fixed axis.Calculate the angular momentum of a rigid body rotating about a fixed axis.Find the total angular momentum and torque about a designated origin of a system of particles.Describe the vector nature of angular momentum.By the end of this section, you will be able to:
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