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You have seen that change in angular momentum depends on the average torque applied and the time interval during which the torque is applied. Plan an experiment similar to the one shown in Figure 10.30 to test the relationship between the change in angular momentum of a system and the product of the average torque applied to the system and the time interval during which the torque is exerted. What would you use as your test system? How could you measure applied torque? What observations could you make to help you analyze changes in angular momentum? Remember that, since angular momentum is a vector, changes can relate to its magnitude or its direction.
This same logic explains the behavior of gyroscopes. [link] shows the two forces acting on a spinning gyroscope. The torque produced is perpendicular to the angular momentum, thus the direction of the torque is changed, but not its magnitude. The gyroscope precesses around a vertical axis, since the torque is always horizontal and perpendicular to . If the gyroscope is not spinning, it acquires angular momentum in the direction of the torque ( ), and it rotates around a horizontal axis, falling over just as we would expect.
Earth itself acts like a gigantic gyroscope. Its angular momentum is along its axis and points at Polaris, the North Star. But Earth is slowly precessing (once in about 26,000 years) due to the torque of the Sun and the Moon on its nonspherical shape.
Rotational kinetic energy is associated with angular momentum? Does that mean that rotational kinetic energy is a vector?
No, energy is always a scalar whether motion is involved or not. No form of energy has a direction in space and you can see that rotational kinetic energy does not depend on the direction of motion just as linear kinetic energy is independent of the direction of motion.
A globe (model of the Earth) is a hollow sphere with a radius of 16 cm. By wrapping a cord around the equator of a globe and pulling on it, a person exerts a torque on the globe of 120 N • m for 1.2 s. What angular momentum does the globe have after 1.2 s?
Since the globe is stationary to start with,
By substituting,
120 N•m • 1.2 s = 144 N•m•s.
The angular momentum of the globe after 1.2 s is 144 N•m•s.
How could you use a fishing reel to test the relationship between the torque applied to a system, the time for which the torque was applied, and the resulting angular momentum of the system? How would you measure angular momentum?
While driving his motorcycle at highway speed, a physics student notices that pulling back lightly on the right handlebar tips the cycle to the left and produces a left turn. Explain why this happens.
Gyroscopes used in guidance systems to indicate directions in space must have an angular momentum that does not change in direction. Yet they are often subjected to large forces and accelerations. How can the direction of their angular momentum be constant when they are accelerated?
Integrated Concepts
The axis of Earth makes a 23.5° angle with a direction perpendicular to the plane of Earth's orbit. As shown in [link] , this axis precesses, making one complete rotation in 25,780 y.
(a) Calculate the change in angular momentum in half this time.
(b) What is the average torque producing this change in angular momentum?
(c) If this torque were created by a single force (it is not) acting at the most effective point on the equator, what would its magnitude be?
(a)
(b)
(c)
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