The angle θ θ is called the angular position of the particle. Its position vector from the origin of the circle to the particle sweeps out the angle θ θ, which increases in the counterclockwise direction as the particle moves along its circular path. The coordinate system is fixed and serves as a frame of reference to define the particle’s position. In Figure 10.2, we show a particle moving in a circle. Although this is the simplest case of rotational motion, it is very useful for many situations, and we use it here to introduce rotational variables. Uniform circular motion (discussed previously in Motion in Two and Three Dimensions) is motion in a circle at constant speed. We will find that rotational motion is described by a set of related variables similar to those we used in translational motion. Now we expand our description of motion to rotation-specifically, rotational motion about a fixed axis. So far in this text, we have mainly studied translational motion, including the variables that describe it: displacement, velocity, and acceleration. Calculate the instantaneous angular acceleration given the angular velocity function.Calculate the average angular acceleration when the angular velocity is changing.Find the angular velocity and angular acceleration in a rotating system.
Calculate the instantaneous angular velocity given the angular position function.Explain how angular velocity is related to tangential speed.Describe the physical meaning of rotational variables as applied to fixed-axis rotation.By the end of this section, you will be able to:
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