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The Greek letter theta, , is used to represent the angle of revolution Figure 8-1 shows the angles in radians for several common fractions of a revolution Note that counterclockwise rotation is designated as positive, while clockwise is negative As an object rotates, the change in the angle is called angular displacement As you know, Earth makes one complete revolution, or 2 rad, in 24 h In 12 h, its rotation is through rad Through what angle does Earth rotate in 6 h Because 6 h is one-fourth of a day, Earth rotates through an angle of rad during that period Earth s rotation as seen from the north pole is 2 positive Is it positive or negative when viewed from the south pole How far does a point on a rotating object move You already found that a point on the edge of an object moves 2 times the radius in one revolution In general, for rotation through an angle, , a point at a distance, r, from the center, as shown in Figure 8-2, moves a distance given by d r If r is measured in meters, you might think that multiplying it by rad would result in d being measured in m rad However, this is not the case Radians indicate the ratio between d and r Thus, d is measured in m



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Answer (for Objective 24): is correct It s legal (although not recommended) to catch an Error It s also legal C for main() to throw an exception The trick to this question is that assertions were not enabled, so line 5 is skipped, and no Error is thrown If the invocation had been "java -ea GiveUp", then answer E would have been correct A, B, D, and E are incorrect based on the above 4 Given:

Figure 8-2 The dashed line shows the path of the point on the CD as the CD rotates counterclockwise about its center





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How fast does a CD spin How do you determine its speed of rotation Recall from 2 that velocity is displacement divided by the time taken to make the displacement Likewise, the angular velocity of an object is angular displacement divided by the time taken to make the displacement Thus, the angular velocity of an object is given by the following equation, where angular velocity is represented by the Greek letter omega, Angular Velocity of an Object

The angular velocity is equal to the angular displacement divided by the time required to make the rotation

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Recall that if the velocity changes over a time interval, the average velocity is not equal to the instantaneous velocity at any given instant Similarly, the angular velocity calculated in this way is actually the average angular velocity over a time interval, t Instantaneous angular velocity is equal to the slope of a graph of angular position versus time Angular velocity is measured in rad/s For Earth, E (2 rad)/ (240 h)(3600 s/h) 727 10 5 rad/s In the same way that counterclockwise rotation produces positive angular displacement, it also results in positive angular velocity If an object s angular velocity is , then the linear velocity of a point a distance, r, from the axis of rotation is given by v r The speed at which an object on Earth s equator moves as a result of Earth s rotation is given by v r (638 106 m)(727 10 5 rad/s) 464 m/s Earth is an example of a rotating, rigid body Even though different points on Earth rotate different distances in each revolution, all points rotate through the same angle All parts of a rigid body rotate at the same rate The Sun, on the other hand, is not a rigid body Different parts of the Sun rotate at different rates Most objects that we will consider in this chapter are rigid bodies

3 import javautil*; 4 public class VC { 5 public static void main(String[] args) { 6 List<Integer> x = new ArrayList<Integer>(); 7 Integer[] a = {3, 1, 4, 1}; 8 x = ArraysasList(a); 9 a[3] = 2; 10 xset(0, 7); 11 for(Integer i: x) Systemoutprint(i + " "); 12 xadd(9); 13 Systemoutprintln(x); 14 } }

used to make the interference pattern in Young s interference experiment (191)

from which we can express the TE-mode impedance:

pointers, a red one and a green one Your friends Mark and Carlos disagree about which has the longer wavelength Mark insists that red light has a longer wavelength, while Carlos is sure that green has the longer wavelength You have a diffraction grating handy Describe what demonstration you would do with this equipment and how you would explain the results to Carlos and Mark to settle their disagreement

of a double-slit interference pattern cannot be used to determine the wavelength of the light waves (191)

What is the result A Compilation fails B 3 1 4 2 [7, 1, 4, 1] C 3 1 4 2 [7, 1, 4, 2] D 7 1 4 2 [7, 1, 4, 2] E F 3 1 4 2 [7, 1, 4, 1, 9] 3 1 4 2 [7, 1, 4, 2, 9]

34 Describe how you could use light of a known wavelength to find the distance between two slits (191)

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