![]() ![]() This result is the basis for defining the units used to measure rotation angles, to be radians (rad), defined so thatĪ comparison of some useful angles expressed in both degrees and radians is shown in Table 6.1. Thus for one complete revolution the rotation angle is We know that for one complete revolution, the arc length is the circumference of a circle of radius. The arc length is the distance traveled along a circular path as shown in Figure 6.3 Note that is the radius of curvature of the circular path. The arc length is described on the circumference. įigure 6.3 The radius of a circle is rotated through an angle. The pits along a line from the center to the edge all move through the same angle in a time. We define the rotation angle to be the ratio of the arc length to the radiusįigure 6.2 All points on a CD travel in circular arcs. The rotation angle is the amount of rotation and is analogous to linear distance. Each pit used to record soundĪlong this line moves through the same angle in the same amount of time. Consider a line from the center of the CD to its edge. When objects rotate about some axis -for example, when the CD (compact disc) in Figure 6.2 rotates about its center -each point in the object follows a circular arc. Motion by defining two angular quantities needed to describe rotational motion. In this chapter, we consider situations where the object does not land but moves in a curve. In which the object is projected into the air, while being subject to the gravitational force, and lands a distance away. Projectile motion is a special case of two-dimensional kinematics Two-Dimensional Kinematics dealt with motion in two dimensions. In Kinematics, we studied motion along a straight line and introduced such concepts as displacement, velocity, and acceleration. Pay attention to the derivation of how angular velocity relates to linear velocity in equations 6.6, 6.7, 6.8, and 6.9. We can relate angular velocity to linear velocity using the relation, with being the radius of curvature. We can write it as, where is the change in angle and is the time it takes for the angle to change that amount. We define angular velocity (or rotational velocity), (the Greek letter omega), as the rate at which the angle changes while an object is rotating. Pay attention to Table 6.1 for conversions between radians and degrees. Radians are the standard unit for physics problems, but we can convert radians to the more familiar degrees for convenience. When describing angles, we often use the unit radian, abbreviated as rad. We call the distance along the circumference traveled ( ) the arc length, and we call the radius of the circular motion ( ) the radius of curvature. We call this the rotational angle, which is defined as. All of the points along this line travel the same angle, in the same amount of time, as the CD spins. ![]() ![]() This figure shows a CD with a line drawn from the center to the edge. To understand circular or rotational motion, picture a spinning disk, such as the picture of a CD in Figure 6.2. ![]()
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