Category: Rotation

As we discussed in Chapter 7, when a force F causes a rigid body of mass m to accelerate along a coordinate axis, the force does work W on the body. Thus, the body’s kinetic energy  can change. Suppose it is the only energy of the body that changes. Then we relate the change ΔK in kinetic energy to the work W with the work–kinetic energy…

A torque can cause rotation of a rigid body, as when you use a torque to rotate a door. Here we want to relate the net torque τnet on a rigid body to the angular acceleration α that torque causes about a rotation axis. We do so by analogy with Newton’s second law (Fnet = ma) for the acceleration a of a body…

A doorknob is located as far as possible from the door’s hinge line for a good reason. If you want to open a heavy door, you must certainly apply a force; that alone, however, is not enough. Where you apply that force and in what direction you push are also important. If you apply your…

If a rigid body consists of a few particles, we can calculate its rotational inertia about a given rotation axis with Eq. 10-33  that is, we can find the product mr2 for each particle and then sum the products. (Recall that r is the perpendicular distance a particle is from the given rotation axis.) If a rigid body consists of a…

The rapidly rotating blade of a table saw certainly has kinetic energy due to that rotation. How can we express the energy? We cannot apply the familiar formula  to the saw as a whole because that would give us the kinetic energy only of the saw’s center of mass, which is zero. Instead, we shall treat…

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…

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…

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…

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…

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…