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Now you re ready to refer to Core Animation classes in your own code. Let s start by modifying the previous example to use explicit animation instead of implicit. To do this, we have to create an instance of a Core Animation class called CABasicAnimation, which is capable of animating between values for any CALayer property which can be animated. In our case, rather than animating the frame, we ll animate the layer s position property. We explicitly set start and end locations for the position using the animation s toValue and fromValue properties. Note that these properties expect a proper object, not just a struct like NSPoint, so we have to wrap each NSPoint value inside an NSValue instance. After creating the animation we add it to the view s layer, along with a key. This key doesn t have anything to do with the property we re animating, it s only there to help us in case we later want to identify this animation. Finally, we change the frame on the view object itself, since the animation only affects the drawing of the view s layer. We want the view to actually move as well, so we have to set its target frame manually. Here s the code to do all of this:

A regulation basketball has a diameter of 241 cm, a mass of 060 kg, and a moment of inertia of 58 10 3 kg m2 The basketball s initial velocity is 25 m/s a What is its initial angular velocity b The ball rolls a total of 12 m How many revolutions does it make c What is its total angular displacement

10 cm lumber Your friend buys a piece of the same size and cuts it into two lengths, each 122 m long, as shown in Figure 8-29 You each carry your lumber on your shoulders a Which load is easier to lift Why b Both you and your friend apply a torque with your hands to keep the lumber from rotating Which load is easier to keep from rotating Why

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after traveling 12 m a If its acceleration was constant, what was its angular acceleration b What torque was acting on it as it was slowing down

244 m

Figure 8-28, is at rest on a surface A rope is wrapped around the cylinder and pulled The cylinder rolls without slipping a After the rope has been pulled a distance of 250 m at a constant speed, how far has the center of mass of the cylinder moved b If the rope was pulled a distance of 250 m in 125 s, how fast was the center of mass of the cylinder moving c What is the angular velocity of the cylinder

- (IBAction)move:(id)sender { NSRect senderFrame = [sender frame]; NSRect superBounds = [[sender superview] bounds]; CABasicAnimation *a = [CABasicAnimation animationWithKeyPath:@"position"]; a.fromValue = [NSValue valueWithPoint:senderFrame.origin]; senderFrame.origin.x = (superBounds.size.width senderFrame.size.width)*drand48(); senderFrame.origin.y = (superBounds.size.height senderFrame.size.height)*drand48(); a.toValue = [NSValue valueWithPoint:senderFrame.origin]; [[sender layer] addAnimation:a forKey:@"position"]; [[sender animator] setFrame:senderFrame]; [sender setFrame:senderFrame]; }

Figure 8-29

is 243 m long and weighs 143 N Paul lifts one end with a force of 57 N a What force must Harris exert b What part of the board should Harris lift

50 m

It rests on two supports, 300 m apart, with equal amounts of the beam extending from each end Suki, who weighs 575 N, stands on the beam in the center and then walks toward one end How close to the end can she come before the beam begins to tip

Figure 8-28

a rotating wheel a Under what conditions can the centripetal acceleration be zero b Under what conditions can the tangential (linear) acceleration be zero c Can the tangential acceleration be nonzero while the centripetal acceleration is zero Explain d Can the centripetal acceleration be nonzero while the tangential acceleration is zero Explain

Note that we also removed the [[sender animator] setFrame:senderFrame]; line from this method, because we don t want to trigger an implicit animation this time. Before this will work, we need to do one more step that the implicit animations took care of for us: establishing layers for the views that need to be animated. Using the animator proxy made this happen automatically, but now we have to turn it on ourselves, for any views that are going to be animated, including the superview of any view that s going to be moving. In our case, this means that the button s superview (the window s content view) needs to be given a layer, and it in turn will establish layers for its subview hierarchy, which is just the button itself. The easiest way to do this is to go back to Interface Builder, select the button in your GUI, and open the Effects Inspector ( 2). At the top of this inspector, you ll see a section titled Wants Core Animation Layer, which shows a list of view objects (see Figure 14 2).

spins at 7200 rpm (revolutions per minute) If the drive is designed to start from rest and reach operating speed in 15 s, what is the angular acceleration of the disk

measure the angular velocity of the transmission and convert it to speed How will increasing the diameter of the tires affect the reading of the speedometer

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