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The user interface classes available in Cocoa cover a wide range of uses, and wherever possible provide consistent APIs for their functionality, so that once you ve learned how to do something with one class, you ll often be able to quickly guess how to achieve similar results with another class In this chapter, we ll cover some of the most common user interface classes that Cocoa provides, showing their basic usage and how you can tailor them to your needs where appropriate Along the way, we ll also touch on some of the auxiliary Cocoa classes that may not always have a tangible screen presence, but still provide important services for your applications We ll be focusing on the following classes (see Figure 4 1 for a sampling of what these objects can look like onscreen): NSTextField: The basic text input method for many applications.

What is the magnitude of an object s centripetal acceleration Compare the triangle made from the position vectors in Figure 6-5b with the triangle made by the velocity vectors in Figure 6-6b The angle between r1 and r2 is the same as that between v1 and v2 Therefore, the two triangles formed by subtracting the two sets of vectors are similar triangles, and the ratios of the lengths of two corresponding sides are equal Thus, r/r v/v The equation is not changed if both sides are divided by t

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Space Elevators Scientists are considering the use of space elevators as a low-cost transportation system to space A cable would be anchored to a station at Earth s equator, and the cable would extend almost 35,800 km from Earth s surface The cable would be attached to a counterweight and would stay extended due to centripetal force Special magnetically powered vehicles would then travel along the cable

Solve this equation for acceleration and give it the special symbol ac , for centripetal acceleration

v2 r Centripetal acceleration always points to the center of the circle Its magnitude is equal to the square of the speed, divided by the radius of motion

Figure 6-7 When the thrower lets go, the hammer initially moves in a straight line that is tangent to the point of release Then it follows a trajectory like that of any object released into the air with an initial horizontal velocity

How can you measure the speed of an object moving in a circle One way is to measure its period, T, the time needed for the object to make one complete revolution During this time, the object travels a distance equal to the circumference of the circle, 2 r The object s speed, then, is represented by v 2 r/T If this expression is substituted for v in the equation for centripetal acceleration, the following equation is obtained ac

Responds to key-presses and renders text Allows a great deal of editing flexibility for the user NSButton: The basic mouse-triggered GUI component Despite their differences in operation and appearance, radio-buttons, checkboxes, and plain old buttons are all instances of NSButton NSPopUpButton: When you have a set of strings you want the user to choose from, an NSPopUpButton is often the way to go..

Because the acceleration of an object moving in a circle is always in the direction of the net force acting on it, there must be a net force toward the center of the circle This force can be provided by any number of agents For Earth circling the Sun, the force is the Sun s gravitational force on Earth, as you ll learn in 7 When a hammer thrower swings the hammer, as in Figure 6-7, the force is the tension in the chain attached to the massive ball When an object moves in a circle, the net force toward the center of the circle is called the centripetal force To accurately analyze centripetal acceleration situations, you must identify the agent of the force that causes the acceleration Then you can apply Newton s second law for the component in the direction of the acceleration in the following way Newton s Second Law for Circular Motion Fnet mac

The net centripetal force on an object moving in a circle is equal to the object s mass, times the centripetal acceleration

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