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These operators return a result of type bool. When performing a comparison between two reference-type objects, the compiler will first look for relational operators defined on the objects (or base classes of the objects). If it finds no applicable operator, and the relational is == or !=, the appropriate relational operator will be called from the object class. This operator compares whether the two operands reference the same instance, not whether they have the same value. For value types, the process is the same if == and != are overloaded. If they aren t overloaded, there s no default implementation for value types, and an error is generated. The overloaded versions of == and != are closely related to the Object.Equals() member. See 29 for more information. For the string type, the relational operators are overloaded, so == and != compare the values of the strings, not the references.

Table 8-1

Linear and Angular Measures Quantity Displacement Velocity Acceleration Linear d (m) v (m/s) a (m/s2) Angular (rad) (rad/s) (rad/s2) Relationship d v a r r r

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1 What is the angular displacement of each of the following hands of a clock in 1 h State your answer in three significant digits a the second hand b the minute hand c the hour hand 2 If a truck has a linear acceleration of 185 m/s2 and the wheels have an angular acceleration of 523 rad/s2, what is the diameter of the truck s wheels 3 The truck in the previous problem is towing a trailer with wheels that have a diameter of 48 cm a How does the linear acceleration of the trailer compare with that of the truck b How do the angular accelerations of the wheels of the trailer and the wheels of the truck compare 4 You want to replace the tires on your car with tires that have a larger diameter After you change the tires, for trips at the same speed and over the same distance, how will the angular velocity and number of revolutions change

Angular frequency A rotating object can make many revolutions in a given amount of time For instance, a spinning wheel can go through several complete revolutions in 1 min Thus, the number of complete revolutions made by the object in 1 s is called angular frequency Angular frequency is f /2 In the next section, you will explore the factors that cause the angular frequency to change

5 Angular Displacement A movie lasts 2 h During that time, what is the angular displacement of each of the following a the hour hand b the minute hand 6 Angular Velocity The Moon rotates once on its axis in 273 days Its radius is 174 106 m a What is the period of the Moon s rotation in seconds b What is the frequency of the Moon s rotation in rad/s c What is the linear speed of a rock on the Moon s equator due only to the Moon s rotation d Compare this speed with the speed of a person on Earth s equator due to Earth s rotation 7 Angular Displacement The ball in a computer mouse is 20 cm in diameter If you move the mouse 12 cm, what is the angular displacement of the ball

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