Category: Center of Mass and Linear Momentum

When two bodies collide, the impulse between them determines the directions in which they then travel. In particular, when the collision is not head-on, the bodies do not end up traveling along their initial axis. For such two-dimensional collisions in a closed, isolated system, the total linear momentum must still be conserved: If the collision…

As we discussed in Section 9-8, everyday collisions are inelastic but we can approximate some of them as being elastic; that is, we can approximate that the total kinetic energy of the colliding bodies is conserved and is not transferred to other forms of energy: This does not mean that the kinetic energy of each colliding…

One-Dimensional Inelastic Collision Figure 9-14 shows two bodies just before and just after they have a one-dimensional collision. The velocities before the collision (subscript i) and after the collision (subscript f) are indicated. The two bodies form our system, which is closed and isolated. We can write the law of conservation of linear momentum for this two-body system…

In Section 9-6, we considered the collision of two particle-like bodies but focused on only one of the bodies at a time. For the next several sections we switch our focus to the system itself, with the assumption that the system is closed and isolated. In Section 9-7, we discussed a rule about such a system: The…

Suppose that the net external force  (and thus the net impulse ) acting on a system of particles is zero (the system is isolated) and that no particles leave or enter the system (the system is closed). Putting  in Eq. 9-27 then yields  or In words,  If no net external force acts on a system of particles, the total linear momentum  of…

The momentum  of any particle-like body cannot change unless a net external force changes it. For example, we could push on the body to change its momentum. More dramatically, we could arrange for the body to collide with a baseball bat. In such a collision (or crash, in everyday language), the external force on the body is brief, has large…

Now that we have defined linear momentum for a single particle, let us extend the definition to a system of particles. Consider a system of n particles, each with its own mass, velocity, and linear momentum. The particles may interact with each other, and external forces may act on them as well. The system as a whole…

In this section, we discuss only a single particle instead of a system of particles, in order to define two important quantities. Then in Section 9-5, we extend those definitions to systems of many particles. The first definition concerns a familiar word—momentum—that has several meanings in everyday language but only a single precise meaning in physics…

Now that we know how to locate the center of mass of a system of particles, we discuss how external forces can move a center of mass. Let us start with a simple system of two billiard balls. If you roll a cue ball at a second billiard ball that is at rest, you expect…

We define the center of mass (com) of a system of particles (such as a person) in order to predict the possible motion of the system.  The center of mass of a system of particles is the point that moves as though (1) all of the system’s mass were concentrated there and (2) all external forces were…