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The angular momentum of an object is equal to the product of the object s moment of inertia and the object s angular velocity

Angular momentum is measured in kg m2/s Just as the linear momentum of an object changes when an impulse acts on it, the angular momentum of an object changes when an angular impulse acts on it Thus, the angular impulse on the object is equal to the change in the object s angular momentum, which is called the angular impulse-angular momentum theorem The angular impulse-angular momentum theorem is represented by the following equation Angular Impulse-Angular Momentum Theorem t Lf Li

The angular impulse on an object is equal to the object s final angular momentum minus the object s initial angular momentum

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Let s start with something simple: enumeration. You re probably familiar with the standard C-based ways of stepping through a list, and perhaps the use of NSEnumerator and even the new fast enumeration ( for in loops) that s been available since the release of Leopard. Now, blocks provide us with yet another way to do the same thing:

If there are no forces acting on an object, its linear momentum is constant If there are no torques acting on an object, its angular momentum is also constant Because an object s mass cannot be changed, if its momentum is constant, then its velocity is also constant In the case of angular momentum, however, the object s angular velocity does not remain constant This is because the moment of inertia depends on the object s mass and the way it is distributed about the axis of rotation or revolution Thus, the angular velocity of an object can change even if no torques are acting on it Consider, for example, a planet orbiting the Sun The torque on the planet is zero because the gravitational force acts directly toward the Sun Therefore, the planet s angular momentum is constant When the distance between the planet and the Sun decreases, however, the planet s moment of inertia of revolution in orbit about the Sun also decreases Thus, the planet s angular velocity increases and it moves faster This is an explanation of Kepler s second law of planetary motion, based on Newton s laws of motion

Figure 9-4 The diver s center of mass is in front of her feet as she gets ready to dive (a) As the diver changes her moment of inertia by moving her arms and legs to increase her angular momentum, the location of the center of mass changes, but the path of the center of mass remains a parabola (b)

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