Author: admin
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Relating the Linear and Angular Variables
In Section 4-7, we discussed uniform circular motion, in which a particle travels at constant linear speed ν along a circle and around an axis of rotation. When a rigid body, such as a merry-go-round, rotates around an axis, each particle in the body moves in its own circle around that axis. Since the body is rigid, all…
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Rotation with Constant Angular Acceleration
In pure translation, motion with a constant linear acceleration (for example, that of a falling body) is an important special case. In Table 2-1, we displayed a series of equations that hold for such motion. In pure rotation, the case of constant angular acceleration is also important, and a parallel set of equations holds for this case also. We shall…
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Are Angular Quantities Vectors?
We can describe the position, velocity, and acceleration of a single particle by means of vectors. If the particle is confined to a straight line, however, we do not really need vector notation. Such a particle has only two directions available to it, and we can indicate these directions with plus and minus signs. In…
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The Rotational Variables
We wish to examine the rotation of a rigid body about a fixed axis. A rigid body is a body that can rotate with all its parts locked together and without any change in its shape. A fixed axis means that the rotation occurs about an axis that does not move. Thus, we shall not examine an object like…
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What Is Physics?
As we have discussed, one focus of physics is motion. However, so far we have examined only the motion of translation, in which an object moves along a straight or curved line, as in Fig. 10-1a. We now turn to the motion of rotation, in which an object turns about an axis, as in Fig. 10-1b. The number of times you…
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Collisions in Two Dimensions
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…
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Elastic Collisions in One Dimension
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…
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Inelastic Collisions in One Dimension
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…
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Momentum and Kinetic Energy in Collisions
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…
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Conservation of Linear Momentum
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…